Wolfram Researchfunctions.wolfram.comOther Wolfram Sites
Search Site
Function CategoriesGraphics GalleryNotationsGeneral IdentitiesAbout This Site Email Comments

View Related Information In
The Documentation Center
MathWorld

Download All Formulas For This Function
Mathematica Notebook
PDF File

Download All Introductions For This Function
Mathematica Notebook
PDF File

 

Developed with Mathematica -- Download a Free Trial Version
 











Cosh






Mathematica Notation

Traditional Notation









Elementary Functions > Cosh[z] > Integration > Indefinite integration > Involving functions of the direct function, hyperbolic, exponential and a power functions > Involving powers of the direct function, hyperbolic, exponential and a power functions > Involving powers of sinh, exp and power > Involving zalpha-1 eb zr+e sinhm(a zr+q) coshv(c zr+g)





http://functions.wolfram.com/01.20.21.4855.01









  


  










Input Form





Integrate[z^(\[Alpha] - 1) E^(b z^r + e) Sinh[a z^r + q]^m Cosh[c z^r + g]^v, z] == (-((I^m 2^(-m - v) z^\[Alpha])/r)) ((E^e Binomial[m, m/2] Binomial[v, v/2] Gamma[\[Alpha]/r, (-b) z^r] (1 - Mod[m, 2]) (1 - Mod[v, 2]))/((-b) z^r)^(\[Alpha]/r) + Binomial[v, v/2] (1 - Mod[v, 2]) Sum[(-1)^k Binomial[m, k] ((E^(e - (I m Pi)/2 - 2 k q + m q) Gamma[\[Alpha]/r, (-b + 2 a k - a m) z^r])/((-b + 2 a k - a m) z^r)^(\[Alpha]/r) + (E^(e + (I m Pi)/2 + 2 k q - m q) Gamma[\[Alpha]/r, (-b - 2 a k + a m) z^r])/((-b - 2 a k + a m) z^r)^(\[Alpha]/r)), {k, 0, Floor[(1/2) (-1 + m)]}] + Binomial[m, m/2] (1 - Mod[m, 2]) Sum[Binomial[v, s] ((E^(e - 2 g s + g v) Gamma[\[Alpha]/r, (-b + 2 c s - c v) z^r])/((-b + 2 c s - c v) z^r)^(\[Alpha]/r) + (E^(e + 2 g s - g v) Gamma[\[Alpha]/r, (-b - 2 c s + c v) z^r])/ ((-b - 2 c s + c v) z^r)^(\[Alpha]/r)), {s, 0, Floor[(1/2) (-1 + v)]}] + Sum[(-1)^k Binomial[m, k] Sum[Binomial[v, s] ((E^(e - (I m Pi)/2 - 2 k q + m q - 2 g s + g v) Gamma[\[Alpha]/r, (-b + 2 a k - a m + 2 c s - c v) z^r])/ ((-b + 2 a k - a m + 2 c s - c v) z^r)^(\[Alpha]/r) + (E^(e + (I m Pi)/2 + 2 k q - m q - 2 g s + g v) Gamma[\[Alpha]/r, (-b - 2 a k + a m + 2 c s - c v) z^r])/ ((-b - 2 a k + a m + 2 c s - c v) z^r)^(\[Alpha]/r) + (E^(e - (I m Pi)/2 - 2 k q + m q + 2 g s - g v) Gamma[\[Alpha]/r, (-b + 2 a k - a m - 2 c s + c v) z^r])/ ((-b + 2 a k - a m - 2 c s + c v) z^r)^(\[Alpha]/r) + (E^(e + (I m Pi)/2 + 2 k q - m q + 2 g s - g v) Gamma[\[Alpha]/r, (-b - 2 a k + a m - 2 c s + c v) z^r])/ ((-b - 2 a k + a m - 2 c s + c v) z^r)^(\[Alpha]/r)), {s, 0, Floor[(1/2) (-1 + v)]}], {k, 0, Floor[(1/2) (-1 + m)]}]) /; Element[m, Integers] && m > 0 && Element[v, Integers] && v > 0










Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["\[Integral]", RowBox[List[SuperscriptBox["z", RowBox[List["\[Alpha]", "-", "1"]]], SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["b", " ", SuperscriptBox["z", "r"]]], "+", "e"]]], SuperscriptBox[RowBox[List["Sinh", "[", RowBox[List[RowBox[List["a", " ", SuperscriptBox["z", "r"]]], "+", "q"]], "]"]], "m"], SuperscriptBox[RowBox[List["Cosh", "[", RowBox[List[RowBox[List["c", " ", SuperscriptBox["z", "r"]]], "+", "g"]], "]"]], "v"], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[RowBox[List["-", FractionBox[RowBox[List[SuperscriptBox["\[ImaginaryI]", "m"], " ", SuperscriptBox["2", RowBox[List[RowBox[List["-", "m"]], "-", "v"]]], SuperscriptBox["z", "\[Alpha]"], " "]], "r"]]], RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", "e"], SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "b"]], " ", SuperscriptBox["z", "r"]]], ")"]], RowBox[List["-", FractionBox["\[Alpha]", "r"]]]], " ", RowBox[List["Binomial", "[", RowBox[List["m", ",", FractionBox["m", "2"]]], "]"]], " ", RowBox[List["Binomial", "[", RowBox[List["v", ",", FractionBox["v", "2"]]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["\[Alpha]", "r"], ",", RowBox[List[RowBox[List["-", "b"]], " ", SuperscriptBox["z", "r"]]]]], "]"]], " ", RowBox[List["(", RowBox[List["1", "-", RowBox[List["Mod", "[", RowBox[List["m", ",", "2"]], "]"]]]], ")"]], " ", RowBox[List["(", RowBox[List["1", "-", RowBox[List["Mod", "[", RowBox[List["v", ",", "2"]], "]"]]]], ")"]]]], "+", RowBox[List[RowBox[List["Binomial", "[", RowBox[List["v", ",", FractionBox["v", "2"]]], "]"]], " ", RowBox[List["(", RowBox[List["1", "-", RowBox[List["Mod", "[", RowBox[List["v", ",", "2"]], "]"]]]], ")"]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], RowBox[List["Floor", "[", RowBox[List[FractionBox["1", "2"], RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "m"]], ")"]]]], "]"]]], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "k"], " ", RowBox[List["Binomial", "[", RowBox[List["m", ",", "k"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["e", "-", FractionBox[RowBox[List["\[ImaginaryI]", " ", "m", " ", "\[Pi]"]], "2"], "-", RowBox[List["2", " ", "k", " ", "q"]], "+", RowBox[List["m", " ", "q"]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "b"]], "+", RowBox[List["2", " ", "a", " ", "k"]], "-", RowBox[List["a", " ", "m"]]]], ")"]], " ", SuperscriptBox["z", "r"]]], ")"]], RowBox[List["-", FractionBox["\[Alpha]", "r"]]]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["\[Alpha]", "r"], ",", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "b"]], "+", RowBox[List["2", " ", "a", " ", "k"]], "-", RowBox[List["a", " ", "m"]]]], ")"]], " ", SuperscriptBox["z", "r"]]]]], "]"]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["e", "+", FractionBox[RowBox[List["\[ImaginaryI]", " ", "m", " ", "\[Pi]"]], "2"], "+", RowBox[List["2", " ", "k", " ", "q"]], "-", RowBox[List["m", " ", "q"]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "b"]], "-", RowBox[List["2", " ", "a", " ", "k"]], "+", RowBox[List["a", " ", "m"]]]], ")"]], " ", SuperscriptBox["z", "r"]]], ")"]], RowBox[List["-", FractionBox["\[Alpha]", "r"]]]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["\[Alpha]", "r"], ",", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "b"]], "-", RowBox[List["2", " ", "a", " ", "k"]], "+", RowBox[List["a", " ", "m"]]]], ")"]], " ", SuperscriptBox["z", "r"]]]]], "]"]]]]]], ")"]]]]]]]], "+", " ", RowBox[List[RowBox[List["Binomial", "[", RowBox[List["m", ",", FractionBox["m", "2"]]], "]"]], " ", RowBox[List["(", RowBox[List["1", "-", RowBox[List["Mod", "[", RowBox[List["m", ",", "2"]], "]"]]]], ")"]], " ", RowBox[List["Sum", "[", " ", RowBox[List[RowBox[List[RowBox[List["Binomial", "[", RowBox[List["v", ",", "s"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["e", "-", RowBox[List["2", " ", "g", " ", "s"]], "+", RowBox[List["g", " ", "v"]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "b"]], "+", RowBox[List["2", " ", "c", " ", "s"]], "-", RowBox[List["c", " ", "v"]]]], ")"]], " ", SuperscriptBox["z", "r"]]], ")"]], RowBox[List["-", FractionBox["\[Alpha]", "r"]]]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["\[Alpha]", "r"], ",", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "b"]], "+", RowBox[List["2", " ", "c", " ", "s"]], "-", RowBox[List["c", " ", "v"]]]], ")"]], " ", SuperscriptBox["z", "r"]]]]], "]"]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["e", "+", RowBox[List["2", " ", "g", " ", "s"]], "-", RowBox[List["g", " ", "v"]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "b"]], "-", RowBox[List["2", " ", "c", " ", "s"]], "+", RowBox[List["c", " ", "v"]]]], ")"]], " ", SuperscriptBox["z", "r"]]], ")"]], RowBox[List["-", FractionBox["\[Alpha]", "r"]]]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["\[Alpha]", "r"], ",", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "b"]], "-", RowBox[List["2", " ", "c", " ", "s"]], "+", RowBox[List["c", " ", "v"]]]], ")"]], " ", SuperscriptBox["z", "r"]]]]], "]"]]]]]], ")"]]]], ",", RowBox[List["{", RowBox[List["s", ",", "0", ",", RowBox[List["Floor", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "v"]], ")"]]]], "]"]]]], "}"]]]], "]"]]]], "+", " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], RowBox[List["Floor", "[", RowBox[List[FractionBox["1", "2"], RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "m"]], ")"]]]], "]"]]], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "k"], " ", RowBox[List["Binomial", "[", RowBox[List["m", ",", "k"]], "]"]], " ", RowBox[List["Sum", "[", " ", RowBox[List[RowBox[List[RowBox[List["Binomial", "[", RowBox[List["v", ",", "s"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["e", "-", FractionBox[RowBox[List["\[ImaginaryI]", " ", "m", " ", "\[Pi]"]], "2"], "-", RowBox[List["2", " ", "k", " ", "q"]], "+", RowBox[List["m", " ", "q"]], "-", RowBox[List["2", " ", "g", " ", "s"]], "+", RowBox[List["g", " ", "v"]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "b"]], "+", RowBox[List["2", " ", "a", " ", "k"]], "-", RowBox[List["a", " ", "m"]], "+", RowBox[List["2", " ", "c", " ", "s"]], "-", RowBox[List["c", " ", "v"]]]], ")"]], " ", SuperscriptBox["z", "r"]]], ")"]], RowBox[List["-", FractionBox["\[Alpha]", "r"]]]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["\[Alpha]", "r"], ",", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "b"]], "+", RowBox[List["2", " ", "a", " ", "k"]], "-", RowBox[List["a", " ", "m"]], "+", RowBox[List["2", " ", "c", " ", "s"]], "-", RowBox[List["c", " ", "v"]]]], ")"]], " ", SuperscriptBox["z", "r"]]]]], "]"]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["e", "+", FractionBox[RowBox[List["\[ImaginaryI]", " ", "m", " ", "\[Pi]"]], "2"], "+", RowBox[List["2", " ", "k", " ", "q"]], "-", RowBox[List["m", " ", "q"]], "-", RowBox[List["2", " ", "g", " ", "s"]], "+", RowBox[List["g", " ", "v"]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "b"]], "-", RowBox[List["2", " ", "a", " ", "k"]], "+", RowBox[List["a", " ", "m"]], "+", RowBox[List["2", " ", "c", " ", "s"]], "-", RowBox[List["c", " ", "v"]]]], ")"]], " ", SuperscriptBox["z", "r"]]], ")"]], RowBox[List["-", FractionBox["\[Alpha]", "r"]]]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["\[Alpha]", "r"], ",", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "b"]], "-", RowBox[List["2", " ", "a", " ", "k"]], "+", RowBox[List["a", " ", "m"]], "+", RowBox[List["2", " ", "c", " ", "s"]], "-", RowBox[List["c", " ", "v"]]]], ")"]], " ", SuperscriptBox["z", "r"]]]]], "]"]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["e", "-", FractionBox[RowBox[List["\[ImaginaryI]", " ", "m", " ", "\[Pi]"]], "2"], "-", RowBox[List["2", " ", "k", " ", "q"]], "+", RowBox[List["m", " ", "q"]], "+", RowBox[List["2", " ", "g", " ", "s"]], "-", RowBox[List["g", " ", "v"]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "b"]], "+", RowBox[List["2", " ", "a", " ", "k"]], "-", RowBox[List["a", " ", "m"]], "-", RowBox[List["2", " ", "c", " ", "s"]], "+", RowBox[List["c", " ", "v"]]]], ")"]], " ", SuperscriptBox["z", "r"]]], ")"]], RowBox[List["-", FractionBox["\[Alpha]", "r"]]]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["\[Alpha]", "r"], ",", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "b"]], "+", RowBox[List["2", " ", "a", " ", "k"]], "-", RowBox[List["a", " ", "m"]], "-", RowBox[List["2", " ", "c", " ", "s"]], "+", RowBox[List["c", " ", "v"]]]], ")"]], " ", SuperscriptBox["z", "r"]]]]], "]"]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["e", "+", FractionBox[RowBox[List["\[ImaginaryI]", " ", "m", " ", "\[Pi]"]], "2"], "+", RowBox[List["2", " ", "k", " ", "q"]], "-", RowBox[List["m", " ", "q"]], "+", RowBox[List["2", " ", "g", " ", "s"]], "-", RowBox[List["g", " ", "v"]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "b"]], "-", RowBox[List["2", " ", "a", " ", "k"]], "+", RowBox[List["a", " ", "m"]], "-", RowBox[List["2", " ", "c", " ", "s"]], "+", RowBox[List["c", " ", "v"]]]], ")"]], " ", SuperscriptBox["z", "r"]]], ")"]], RowBox[List["-", FractionBox["\[Alpha]", "r"]]]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["\[Alpha]", "r"], ",", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "b"]], "-", RowBox[List["2", " ", "a", " ", "k"]], "+", RowBox[List["a", " ", "m"]], "-", RowBox[List["2", " ", "c", " ", "s"]], "+", RowBox[List["c", " ", "v"]]]], ")"]], " ", SuperscriptBox["z", "r"]]]]], "]"]]]]]], ")"]]]], ",", RowBox[List["{", RowBox[List["s", ",", "0", ",", RowBox[List["Floor", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "v"]], ")"]]]], "]"]]]], "}"]]]], "]"]]]]]]]], ")"]]]]]], "/;", RowBox[List[RowBox[List["m", "\[Element]", "Integers"]], "\[And]", RowBox[List["m", ">", "0"]], "\[And]", RowBox[List["v", "\[Element]", "Integers"]], "\[And]", RowBox[List["v", ">", "0"]]]]]]]]










MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <mo> &#8747; </mo> <mrow> <mrow> <msup> <mi> z </mi> <mrow> <mi> &#945; </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> &#8290; </mo> <msup> <mi> &#8519; </mi> <mrow> <mrow> <mi> b </mi> <mo> &#8290; </mo> <msup> <mi> z </mi> <mi> r </mi> </msup> </mrow> <mo> + </mo> <mi> e </mi> </mrow> </msup> <mo> &#8290; </mo> <mrow> <msup> <mi> sinh </mi> <mi> m </mi> </msup> <mo> ( </mo> <mrow> <mrow> <mi> a </mi> <mo> &#8290; </mo> <msup> <mi> z </mi> <mi> r </mi> </msup> </mrow> <mo> + </mo> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <msup> <mi> cosh </mi> <mi> v </mi> </msup> <mo> ( </mo> <mrow> <mrow> <mi> c </mi> <mo> &#8290; </mo> <msup> <mi> z </mi> <mi> r </mi> </msup> </mrow> <mo> + </mo> <mi> g </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> &#8290; </mo> <mrow> <mo> &#8518; </mo> <mi> z </mi> </mrow> </mrow> </mrow> <mo> &#10869; </mo> <mrow> <mrow> <mo> - </mo> <mfrac> <mrow> <msup> <mi> &#8520; </mi> <mi> m </mi> </msup> <mo> &#8290; </mo> <msup> <mn> 2 </mn> <mrow> <mrow> <mo> - </mo> <mi> m </mi> </mrow> <mo> - </mo> <mi> v </mi> </mrow> </msup> <mo> &#8290; </mo> <msup> <mi> z </mi> <mi> &#945; </mi> </msup> </mrow> <mi> r </mi> </mfrac> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msup> <mi> &#8519; </mi> <mi> e </mi> </msup> <mo> &#8290; </mo> <semantics> <mrow> <mo> ( </mo> <mtable> <mtr> <mtd> <mi> m </mi> </mtd> </mtr> <mtr> <mtd> <mfrac> <mi> m </mi> <mn> 2 </mn> </mfrac> </mtd> </mtr> </mtable> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;(&quot;, GridBox[List[List[TagBox[&quot;m&quot;, Identity]], List[TagBox[FractionBox[&quot;m&quot;, &quot;2&quot;], Identity]]]], &quot;)&quot;]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] </annotation> </semantics> <mo> &#8290; </mo> <semantics> <mrow> <mo> ( </mo> <mtable> <mtr> <mtd> <mi> v </mi> </mtd> </mtr> <mtr> <mtd> <mfrac> <mi> v </mi> <mn> 2 </mn> </mfrac> </mtd> </mtr> </mtable> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;(&quot;, GridBox[List[List[TagBox[&quot;v&quot;, Identity]], List[TagBox[FractionBox[&quot;v&quot;, &quot;2&quot;], Identity]]]], &quot;)&quot;]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] </annotation> </semantics> <mo> &#8290; </mo> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mfrac> <mi> &#945; </mi> <mi> r </mi> </mfrac> <mo> , </mo> <mrow> <mrow> <mo> - </mo> <mi> b </mi> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mi> r </mi> </msup> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <semantics> <mrow> <mi> m </mi> <mo> &#8290; </mo> <mi> mod </mi> <mo> &#8290; </mo> <mn> 2 </mn> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <rem /> <ci> $CellContext`m </ci> <cn type='integer'> 2 </cn> </apply> </annotation-xml> </semantics> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <semantics> <mrow> <mi> v </mi> <mo> &#8290; </mo> <mi> mod </mi> <mo> &#8290; </mo> <mn> 2 </mn> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <rem /> <ci> $CellContext`v </ci> <cn type='integer'> 2 </cn> </apply> </annotation-xml> </semantics> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> b </mi> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mi> r </mi> </msup> </mrow> <mo> ) </mo> </mrow> <mrow> <mo> - </mo> <mfrac> <mi> &#945; </mi> <mi> r </mi> </mfrac> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <semantics> <mrow> <mo> ( </mo> <mtable> <mtr> <mtd> <mi> v </mi> </mtd> </mtr> <mtr> <mtd> <mfrac> <mi> v </mi> <mn> 2 </mn> </mfrac> </mtd> </mtr> </mtable> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;(&quot;, GridBox[List[List[TagBox[&quot;v&quot;, Identity]], List[TagBox[FractionBox[&quot;v&quot;, &quot;2&quot;], Identity]]]], &quot;)&quot;]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] </annotation> </semantics> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <semantics> <mrow> <mi> v </mi> <mo> &#8290; </mo> <mi> mod </mi> <mo> &#8290; </mo> <mn> 2 </mn> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <rem /> <ci> $CellContext`v </ci> <cn type='integer'> 2 </cn> </apply> </annotation-xml> </semantics> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mrow> <mo> &#8970; </mo> <mfrac> <mrow> <mi> m </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mn> 2 </mn> </mfrac> <mo> &#8971; </mo> </mrow> </munderover> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> k </mi> </msup> <mo> &#8290; </mo> <semantics> <mrow> <mo> ( </mo> <mtable> <mtr> <mtd> <mi> m </mi> </mtd> </mtr> <mtr> <mtd> <mi> k </mi> </mtd> </mtr> </mtable> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;(&quot;, GridBox[List[List[TagBox[&quot;m&quot;, Identity]], List[TagBox[&quot;k&quot;, Identity]]]], &quot;)&quot;]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] </annotation> </semantics> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msup> <mi> &#8519; </mi> <mrow> <mi> e </mi> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> k </mi> <mo> &#8290; </mo> <mi> q </mi> </mrow> <mo> - </mo> <mrow> <mi> m </mi> <mo> &#8290; </mo> <mi> q </mi> </mrow> <mo> + </mo> <mfrac> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> m </mi> <mo> &#8290; </mo> <mi> &#960; </mi> </mrow> <mn> 2 </mn> </mfrac> </mrow> </msup> <mo> &#8290; </mo> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mfrac> <mi> &#945; </mi> <mi> r </mi> </mfrac> <mo> , </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> b </mi> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> a </mi> <mo> &#8290; </mo> <mi> k </mi> </mrow> <mo> + </mo> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mi> m </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mi> r </mi> </msup> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> b </mi> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> a </mi> <mo> &#8290; </mo> <mi> k </mi> </mrow> <mo> + </mo> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mi> m </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mi> r </mi> </msup> </mrow> <mo> ) </mo> </mrow> <mrow> <mo> - </mo> <mfrac> <mi> &#945; </mi> <mi> r </mi> </mfrac> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <msup> <mi> &#8519; </mi> <mrow> <mi> e </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> k </mi> <mo> &#8290; </mo> <mi> q </mi> </mrow> <mo> + </mo> <mrow> <mi> m </mi> <mo> &#8290; </mo> <mi> q </mi> </mrow> <mo> - </mo> <mfrac> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> m </mi> <mo> &#8290; </mo> <mi> &#960; </mi> </mrow> <mn> 2 </mn> </mfrac> </mrow> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> b </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> a </mi> <mo> &#8290; </mo> <mi> k </mi> </mrow> <mo> - </mo> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mi> m </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mi> r </mi> </msup> </mrow> <mo> ) </mo> </mrow> <mrow> <mo> - </mo> <mfrac> <mi> &#945; </mi> <mi> r </mi> </mfrac> </mrow> </msup> <mo> &#8290; </mo> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mfrac> <mi> &#945; </mi> <mi> r </mi> </mfrac> <mo> , </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> b </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> a </mi> <mo> &#8290; </mo> <mi> k </mi> </mrow> <mo> - </mo> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mi> m </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mi> r </mi> </msup> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <mo> + </mo> <mrow> <semantics> <mrow> <mo> ( </mo> <mtable> <mtr> <mtd> <mi> m </mi> </mtd> </mtr> <mtr> <mtd> <mfrac> <mi> m </mi> <mn> 2 </mn> </mfrac> </mtd> </mtr> </mtable> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;(&quot;, GridBox[List[List[TagBox[&quot;m&quot;, Identity]], List[TagBox[FractionBox[&quot;m&quot;, &quot;2&quot;], Identity]]]], &quot;)&quot;]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] </annotation> </semantics> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <semantics> <mrow> <mi> m </mi> <mo> &#8290; </mo> <mi> mod </mi> <mo> &#8290; </mo> <mn> 2 </mn> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <rem /> <ci> $CellContext`m </ci> <cn type='integer'> 2 </cn> </apply> </annotation-xml> </semantics> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <mi> s </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mrow> <mo> &#8970; </mo> <mfrac> <mrow> <mi> v </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mn> 2 </mn> </mfrac> <mo> &#8971; </mo> </mrow> </munderover> <mrow> <semantics> <mrow> <mo> ( </mo> <mtable> <mtr> <mtd> <mi> v </mi> </mtd> </mtr> <mtr> <mtd> <mi> s </mi> </mtd> </mtr> </mtable> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;(&quot;, GridBox[List[List[TagBox[&quot;v&quot;, Identity]], List[TagBox[&quot;s&quot;, Identity]]]], &quot;)&quot;]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] </annotation> </semantics> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msup> <mi> &#8519; </mi> <mrow> <mi> e </mi> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> g </mi> <mo> &#8290; </mo> <mi> s </mi> </mrow> <mo> - </mo> <mrow> <mi> g </mi> <mo> &#8290; </mo> <mi> v </mi> </mrow> </mrow> </msup> <mo> &#8290; </mo> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mfrac> <mi> &#945; </mi> <mi> r </mi> </mfrac> <mo> , </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> b </mi> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> c </mi> <mo> &#8290; </mo> <mi> s </mi> </mrow> <mo> + </mo> <mrow> <mi> c </mi> <mo> &#8290; </mo> <mi> v </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mi> r </mi> </msup> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> b </mi> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> c </mi> <mo> &#8290; </mo> <mi> s </mi> </mrow> <mo> + </mo> <mrow> <mi> c </mi> <mo> &#8290; </mo> <mi> v </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mi> r </mi> </msup> </mrow> <mo> ) </mo> </mrow> <mrow> <mo> - </mo> <mfrac> <mi> &#945; </mi> <mi> r </mi> </mfrac> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <msup> <mi> &#8519; </mi> <mrow> <mi> e </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> g </mi> <mo> &#8290; </mo> <mi> s </mi> </mrow> <mo> + </mo> <mrow> <mi> g </mi> <mo> &#8290; </mo> <mi> v </mi> </mrow> </mrow> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> b </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> c </mi> <mo> &#8290; </mo> <mi> s </mi> </mrow> <mo> - </mo> <mrow> <mi> c </mi> <mo> &#8290; </mo> <mi> v </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mi> r </mi> </msup> </mrow> <mo> ) </mo> </mrow> <mrow> <mo> - </mo> <mfrac> <mi> &#945; </mi> <mi> r </mi> </mfrac> </mrow> </msup> <mo> &#8290; </mo> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mfrac> <mi> &#945; </mi> <mi> r </mi> </mfrac> <mo> , </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> b </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> c </mi> <mo> &#8290; </mo> <mi> s </mi> </mrow> <mo> - </mo> <mrow> <mi> c </mi> <mo> &#8290; </mo> <mi> v </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mi> r </mi> </msup> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <mo> + </mo> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mrow> <mo> &#8970; </mo> <mfrac> <mrow> <mi> m </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mn> 2 </mn> </mfrac> <mo> &#8971; </mo> </mrow> </munderover> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> k </mi> </msup> <mo> &#8290; </mo> <semantics> <mrow> <mo> ( </mo> <mtable> <mtr> <mtd> <mi> m </mi> </mtd> </mtr> <mtr> <mtd> <mi> k </mi> </mtd> </mtr> </mtable> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;(&quot;, GridBox[List[List[TagBox[&quot;m&quot;, Identity]], List[TagBox[&quot;k&quot;, Identity]]]], &quot;)&quot;]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] </annotation> </semantics> <mo> &#8290; </mo> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <mi> s </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mrow> <mo> &#8970; </mo> <mfrac> <mrow> <mi> v </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mn> 2 </mn> </mfrac> <mo> &#8971; </mo> </mrow> </munderover> <mrow> <semantics> <mrow> <mo> ( </mo> <mtable> <mtr> <mtd> <mi> v </mi> </mtd> </mtr> <mtr> <mtd> <mi> s </mi> </mtd> </mtr> </mtable> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;(&quot;, GridBox[List[List[TagBox[&quot;v&quot;, Identity]], List[TagBox[&quot;s&quot;, Identity]]]], &quot;)&quot;]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] </annotation> </semantics> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msup> <mi> &#8519; </mi> <mrow> <mi> e </mi> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> k </mi> <mo> &#8290; </mo> <mi> q </mi> </mrow> <mo> - </mo> <mrow> <mi> m </mi> <mo> &#8290; </mo> <mi> q </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> g </mi> <mo> &#8290; </mo> <mi> s </mi> </mrow> <mo> - </mo> <mrow> <mi> g </mi> <mo> &#8290; </mo> <mi> v </mi> </mrow> <mo> + </mo> <mfrac> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> m </mi> <mo> &#8290; </mo> <mi> &#960; </mi> </mrow> <mn> 2 </mn> </mfrac> </mrow> </msup> <mo> &#8290; </mo> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mfrac> <mi> &#945; </mi> <mi> r </mi> </mfrac> <mo> , </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> b </mi> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> a </mi> <mo> &#8290; </mo> <mi> k </mi> </mrow> <mo> + </mo> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mi> m </mi> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> c </mi> <mo> &#8290; </mo> <mi> s </mi> </mrow> <mo> + </mo> <mrow> <mi> c </mi> <mo> &#8290; </mo> <mi> v </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mi> r </mi> </msup> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> b </mi> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> a </mi> <mo> &#8290; </mo> <mi> k </mi> </mrow> <mo> + </mo> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mi> m </mi> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> c </mi> <mo> &#8290; </mo> <mi> s </mi> </mrow> <mo> + </mo> <mrow> <mi> c </mi> <mo> &#8290; </mo> <mi> v </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mi> r </mi> </msup> </mrow> <mo> ) </mo> </mrow> <mrow> <mo> - </mo> <mfrac> <mi> &#945; </mi> <mi> r </mi> </mfrac> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <msup> <mi> &#8519; </mi> <mrow> <mi> e </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> k </mi> <mo> &#8290; </mo> <mi> q </mi> </mrow> <mo> + </mo> <mrow> <mi> m </mi> <mo> &#8290; </mo> <mi> q </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> g </mi> <mo> &#8290; </mo> <mi> s </mi> </mrow> <mo> - </mo> <mrow> <mi> g </mi> <mo> &#8290; </mo> <mi> v </mi> </mrow> <mo> - </mo> <mfrac> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> m </mi> <mo> &#8290; </mo> <mi> &#960; </mi> </mrow> <mn> 2 </mn> </mfrac> </mrow> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> b </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> a </mi> <mo> &#8290; </mo> <mi> k </mi> </mrow> <mo> - </mo> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mi> m </mi> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> c </mi> <mo> &#8290; </mo> <mi> s </mi> </mrow> <mo> + </mo> <mrow> <mi> c </mi> <mo> &#8290; </mo> <mi> v </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mi> r </mi> </msup> </mrow> <mo> ) </mo> </mrow> <mrow> <mo> - </mo> <mfrac> <mi> &#945; </mi> <mi> r </mi> </mfrac> </mrow> </msup> <mo> &#8290; </mo> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mfrac> <mi> &#945; </mi> <mi> r </mi> </mfrac> <mo> , </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> b </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> a </mi> <mo> &#8290; </mo> <mi> k </mi> </mrow> <mo> - </mo> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mi> m </mi> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> c </mi> <mo> &#8290; </mo> <mi> s </mi> </mrow> <mo> + </mo> <mrow> <mi> c </mi> <mo> &#8290; </mo> <mi> v </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mi> r </mi> </msup> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <msup> <mi> &#8519; </mi> <mrow> <mi> e </mi> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> k </mi> <mo> &#8290; </mo> <mi> q </mi> </mrow> <mo> - </mo> <mrow> <mi> m </mi> <mo> &#8290; </mo> <mi> q </mi> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> g </mi> <mo> &#8290; </mo> <mi> s </mi> </mrow> <mo> + </mo> <mrow> <mi> g </mi> <mo> &#8290; </mo> <mi> v </mi> </mrow> <mo> + </mo> <mfrac> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> m </mi> <mo> &#8290; </mo> <mi> &#960; </mi> </mrow> <mn> 2 </mn> </mfrac> </mrow> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> b </mi> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> a </mi> <mo> &#8290; </mo> <mi> k </mi> </mrow> <mo> + </mo> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mi> m </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> c </mi> <mo> &#8290; </mo> <mi> s </mi> </mrow> <mo> - </mo> <mrow> <mi> c </mi> <mo> &#8290; </mo> <mi> v </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mi> r </mi> </msup> </mrow> <mo> ) </mo> </mrow> <mrow> <mo> - </mo> <mfrac> <mi> &#945; </mi> <mi> r </mi> </mfrac> </mrow> </msup> <mo> &#8290; </mo> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mfrac> <mi> &#945; </mi> <mi> r </mi> </mfrac> <mo> , </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> b </mi> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> a </mi> <mo> &#8290; </mo> <mi> k </mi> </mrow> <mo> + </mo> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mi> m </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> c </mi> <mo> &#8290; </mo> <mi> s </mi> </mrow> <mo> - </mo> <mrow> <mi> c </mi> <mo> &#8290; </mo> <mi> v </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mi> r </mi> </msup> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <msup> <mi> &#8519; </mi> <mrow> <mi> e </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> k </mi> <mo> &#8290; </mo> <mi> q </mi> </mrow> <mo> + </mo> <mrow> <mi> m </mi> <mo> &#8290; </mo> <mi> q </mi> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> g </mi> <mo> &#8290; </mo> <mi> s </mi> </mrow> <mo> + </mo> <mrow> <mi> g </mi> <mo> &#8290; </mo> <mi> v </mi> </mrow> <mo> - </mo> <mfrac> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> m </mi> <mo> &#8290; </mo> <mi> &#960; </mi> </mrow> <mn> 2 </mn> </mfrac> </mrow> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> b </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> a </mi> <mo> &#8290; </mo> <mi> k </mi> </mrow> <mo> - </mo> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mi> m </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> c </mi> <mo> &#8290; </mo> <mi> s </mi> </mrow> <mo> - </mo> <mrow> <mi> c </mi> <mo> &#8290; </mo> <mi> v </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mi> r </mi> </msup> </mrow> <mo> ) </mo> </mrow> <mrow> <mo> - </mo> <mfrac> <mi> &#945; </mi> <mi> r </mi> </mfrac> </mrow> </msup> <mo> &#8290; </mo> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mfrac> <mi> &#945; </mi> <mi> r </mi> </mfrac> <mo> , </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> b </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> a </mi> <mo> &#8290; </mo> <mi> k </mi> </mrow> <mo> - </mo> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mi> m </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> c </mi> <mo> &#8290; </mo> <mi> s </mi> </mrow> <mo> - </mo> <mrow> <mi> c </mi> <mo> &#8290; </mo> <mi> v </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mi> r </mi> </msup> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> m </mi> <mo> &#8712; </mo> <msup> <mi> &#8469; </mi> <mo> + </mo> </msup> </mrow> <mo> &#8743; </mo> <mrow> <mi> v </mi> <mo> &#8712; </mo> <msup> <mi> &#8469; </mi> <mo> + </mo> </msup> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <int /> <bvar> <ci> z </ci> </bvar> <apply> <times /> <apply> <power /> <ci> z </ci> <apply> <plus /> <ci> &#945; </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <exponentiale /> <apply> <plus /> <apply> <times /> <ci> b </ci> <apply> <power /> <ci> z </ci> <ci> r </ci> </apply> </apply> <ci> e </ci> </apply> </apply> <apply> <power /> <apply> <sinh /> <apply> <plus /> <apply> <times /> <ci> a </ci> <apply> <power /> <ci> z </ci> <ci> r </ci> </apply> </apply> <ci> q </ci> </apply> </apply> <ci> m </ci> </apply> <apply> <power /> <apply> <cosh /> <apply> <plus /> <apply> <times /> <ci> c </ci> <apply> <power /> <ci> z </ci> <ci> r </ci> </apply> </apply> <ci> g </ci> </apply> </apply> <ci> v </ci> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <imaginaryi /> <ci> m </ci> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> m </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> v </ci> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <ci> &#945; </ci> </apply> <apply> <power /> <ci> r </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <power /> <exponentiale /> <ci> e </ci> </apply> <apply> <ci> Binomial </ci> <ci> m </ci> <apply> <times /> <ci> m </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <ci> Binomial </ci> <ci> v </ci> <apply> <times /> <ci> v </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <ci> Gamma </ci> <apply> <times /> <ci> &#945; </ci> <apply> <power /> <ci> r </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> <apply> <power /> <ci> z </ci> <ci> r </ci> </apply> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <rem /> <ci> $CellContext`m </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <rem /> <ci> $CellContext`v </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> <apply> <power /> <ci> z </ci> <ci> r </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> &#945; </ci> <apply> <power /> <ci> r </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <ci> Binomial </ci> <ci> v </ci> <apply> <times /> <ci> v </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <rem /> <ci> $CellContext`v </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <sum /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <apply> <floor /> <apply> <times /> <apply> <plus /> <ci> m </ci> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </uplimit> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <ci> k </ci> </apply> <apply> <ci> Binomial </ci> <ci> m </ci> <ci> k </ci> </apply> <apply> <plus /> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <plus /> <ci> e </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> k </ci> <ci> q </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> m </ci> <ci> q </ci> </apply> </apply> <apply> <times /> <imaginaryi /> <ci> m </ci> <pi /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <ci> Gamma </ci> <apply> <times /> <ci> &#945; </ci> <apply> <power /> <ci> r </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> <ci> k </ci> </apply> </apply> <apply> <times /> <ci> a </ci> <ci> m </ci> </apply> </apply> <apply> <power /> <ci> z </ci> <ci> r </ci> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> <ci> k </ci> </apply> </apply> <apply> <times /> <ci> a </ci> <ci> m </ci> </apply> </apply> <apply> <power /> <ci> z </ci> <ci> r </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> &#945; </ci> <apply> <power /> <ci> r </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <plus /> <ci> e </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> k </ci> <ci> q </ci> </apply> </apply> <apply> <times /> <ci> m </ci> <ci> q </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> m </ci> <pi /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> <ci> k </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> a </ci> <ci> m </ci> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <ci> r </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> &#945; </ci> <apply> <power /> <ci> r </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <ci> Gamma </ci> <apply> <times /> <ci> &#945; </ci> <apply> <power /> <ci> r </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> <ci> k </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> a </ci> <ci> m </ci> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <ci> r </ci> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <ci> Binomial </ci> <ci> m </ci> <apply> <times /> <ci> m </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <rem /> <ci> $CellContext`m </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <sum /> <bvar> <ci> s </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <apply> <floor /> <apply> <times /> <apply> <plus /> <ci> v </ci> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </uplimit> <apply> <times /> <apply> <ci> Binomial </ci> <ci> v </ci> <ci> s </ci> </apply> <apply> <plus /> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <plus /> <ci> e </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> g </ci> <ci> s </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> g </ci> <ci> v </ci> </apply> </apply> </apply> </apply> <apply> <ci> Gamma </ci> <apply> <times /> <ci> &#945; </ci> <apply> <power /> <ci> r </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> <ci> s </ci> </apply> </apply> <apply> <times /> <ci> c </ci> <ci> v </ci> </apply> </apply> <apply> <power /> <ci> z </ci> <ci> r </ci> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> <ci> s </ci> </apply> </apply> <apply> <times /> <ci> c </ci> <ci> v </ci> </apply> </apply> <apply> <power /> <ci> z </ci> <ci> r </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> &#945; </ci> <apply> <power /> <ci> r </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <plus /> <ci> e </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> g </ci> <ci> s </ci> </apply> </apply> <apply> <times /> <ci> g </ci> <ci> v </ci> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> <ci> s </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> c </ci> <ci> v </ci> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <ci> r </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> &#945; </ci> <apply> <power /> <ci> r </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <ci> Gamma </ci> <apply> <times /> <ci> &#945; </ci> <apply> <power /> <ci> r </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> <ci> s </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> c </ci> <ci> v </ci> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <ci> r </ci> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <sum /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <apply> <floor /> <apply> <times /> <apply> <plus /> <ci> m </ci> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </uplimit> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <ci> k </ci> </apply> <apply> <ci> Binomial </ci> <ci> m </ci> <ci> k </ci> </apply> <apply> <sum /> <bvar> <ci> s </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <apply> <floor /> <apply> <times /> <apply> <plus /> <ci> v </ci> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </uplimit> <apply> <times /> <apply> <ci> Binomial </ci> <ci> v </ci> <ci> s </ci> </apply> <apply> <plus /> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <plus /> <ci> e </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> k </ci> <ci> q </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> m </ci> <ci> q </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <ci> g </ci> <ci> s </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> g </ci> <ci> v </ci> </apply> </apply> <apply> <times /> <imaginaryi /> <ci> m </ci> <pi /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <ci> Gamma </ci> <apply> <times /> <ci> &#945; </ci> <apply> <power /> <ci> r </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> <ci> k </ci> </apply> </apply> <apply> <times /> <ci> a </ci> <ci> m </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> <ci> s </ci> </apply> </apply> <apply> <times /> <ci> c </ci> <ci> v </ci> </apply> </apply> <apply> <power /> <ci> z </ci> <ci> r </ci> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> <ci> k </ci> </apply> </apply> <apply> <times /> <ci> a </ci> <ci> m </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> <ci> s </ci> </apply> </apply> <apply> <times /> <ci> c </ci> <ci> v </ci> </apply> </apply> <apply> <power /> <ci> z </ci> <ci> r </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> &#945; </ci> <apply> <power /> <ci> r </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <plus /> <ci> e </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> k </ci> <ci> q </ci> </apply> </apply> <apply> <times /> <ci> m </ci> <ci> q </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <ci> g </ci> <ci> s </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> g </ci> <ci> v </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> m </ci> <pi /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> <ci> k </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> a </ci> <ci> m </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> <ci> s </ci> </apply> </apply> <apply> <times /> <ci> c </ci> <ci> v </ci> </apply> </apply> <apply> <power /> <ci> z </ci> <ci> r </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> &#945; </ci> <apply> <power /> <ci> r </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <ci> Gamma </ci> <apply> <times /> <ci> &#945; </ci> <apply> <power /> <ci> r </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> <ci> k </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> a </ci> <ci> m </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> <ci> s </ci> </apply> </apply> <apply> <times /> <ci> c </ci> <ci> v </ci> </apply> </apply> <apply> <power /> <ci> z </ci> <ci> r </ci> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <plus /> <ci> e </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> k </ci> <ci> q </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> m </ci> <ci> q </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> g </ci> <ci> s </ci> </apply> </apply> <apply> <times /> <ci> g </ci> <ci> v </ci> </apply> <apply> <times /> <imaginaryi /> <ci> m </ci> <pi /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> <ci> k </ci> </apply> </apply> <apply> <times /> <ci> a </ci> <ci> m </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> <ci> s </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> c </ci> <ci> v </ci> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <ci> r </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> &#945; </ci> <apply> <power /> <ci> r </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <ci> Gamma </ci> <apply> <times /> <ci> &#945; </ci> <apply> <power /> <ci> r </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> <ci> k </ci> </apply> </apply> <apply> <times /> <ci> a </ci> <ci> m </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> <ci> s </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> c </ci> <ci> v </ci> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <ci> r </ci> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <plus /> <ci> e </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> k </ci> <ci> q </ci> </apply> </apply> <apply> <times /> <ci> m </ci> <ci> q </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> g </ci> <ci> s </ci> </apply> </apply> <apply> <times /> <ci> g </ci> <ci> v </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> m </ci> <pi /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> <ci> k </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> a </ci> <ci> m </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> <ci> s </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> c </ci> <ci> v </ci> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <ci> r </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> &#945; </ci> <apply> <power /> <ci> r </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <ci> Gamma </ci> <apply> <times /> <ci> &#945; </ci> <apply> <power /> <ci> r </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> <ci> k </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> a </ci> <ci> m </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> <ci> s </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> c </ci> <ci> v </ci> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <ci> r </ci> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <and /> <apply> <in /> <ci> m </ci> <apply> <ci> SuperPlus </ci> <ci> &#8469; </ci> </apply> </apply> <apply> <in /> <ci> v </ci> <apply> <ci> SuperPlus </ci> <ci> &#8469; </ci> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List[SuperscriptBox["z_", RowBox[List["\[Alpha]_", "-", "1"]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["b_", " ", SuperscriptBox["z_", "r_"]]], "+", "e_"]]], " ", SuperscriptBox[RowBox[List["Sinh", "[", RowBox[List[RowBox[List["a_", " ", SuperscriptBox["z_", "r_"]]], "+", "q_"]], "]"]], "m_"], " ", SuperscriptBox[RowBox[List["Cosh", "[", RowBox[List[RowBox[List["c_", " ", SuperscriptBox["z_", "r_"]]], "+", "g_"]], "]"]], "v_"]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["\[ImaginaryI]", "m"], " ", SuperscriptBox["2", RowBox[List[RowBox[List["-", "m"]], "-", "v"]]], " ", SuperscriptBox["z", "\[Alpha]"]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", "e"], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "b"]], " ", SuperscriptBox["z", "r"]]], ")"]], RowBox[List["-", FractionBox["\[Alpha]", "r"]]]], " ", RowBox[List["Binomial", "[", RowBox[List["m", ",", FractionBox["m", "2"]]], "]"]], " ", RowBox[List["Binomial", "[", RowBox[List["v", ",", FractionBox["v", "2"]]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["\[Alpha]", "r"], ",", RowBox[List[RowBox[List["-", "b"]], " ", SuperscriptBox["z", "r"]]]]], "]"]], " ", RowBox[List["(", RowBox[List["1", "-", RowBox[List["Mod", "[", RowBox[List["m", ",", "2"]], "]"]]]], ")"]], " ", RowBox[List["(", RowBox[List["1", "-", RowBox[List["Mod", "[", RowBox[List["v", ",", "2"]], "]"]]]], ")"]]]], "+", RowBox[List[RowBox[List["Binomial", "[", RowBox[List["v", ",", FractionBox["v", "2"]]], "]"]], " ", RowBox[List["(", RowBox[List["1", "-", RowBox[List["Mod", "[", RowBox[List["v", ",", "2"]], "]"]]]], ")"]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], RowBox[List["Floor", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "m"]], ")"]]]], "]"]]], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "k"], " ", RowBox[List["Binomial", "[", RowBox[List["m", ",", "k"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["e", "-", FractionBox[RowBox[List["\[ImaginaryI]", " ", "m", " ", "\[Pi]"]], "2"], "-", RowBox[List["2", " ", "k", " ", "q"]], "+", RowBox[List["m", " ", "q"]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "b"]], "+", RowBox[List["2", " ", "a", " ", "k"]], "-", RowBox[List["a", " ", "m"]]]], ")"]], " ", SuperscriptBox["z", "r"]]], ")"]], RowBox[List["-", FractionBox["\[Alpha]", "r"]]]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["\[Alpha]", "r"], ",", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "b"]], "+", RowBox[List["2", " ", "a", " ", "k"]], "-", RowBox[List["a", " ", "m"]]]], ")"]], " ", SuperscriptBox["z", "r"]]]]], "]"]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["e", "+", FractionBox[RowBox[List["\[ImaginaryI]", " ", "m", " ", "\[Pi]"]], "2"], "+", RowBox[List["2", " ", "k", " ", "q"]], "-", RowBox[List["m", " ", "q"]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "b"]], "-", RowBox[List["2", " ", "a", " ", "k"]], "+", RowBox[List["a", " ", "m"]]]], ")"]], " ", SuperscriptBox["z", "r"]]], ")"]], RowBox[List["-", FractionBox["\[Alpha]", "r"]]]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["\[Alpha]", "r"], ",", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "b"]], "-", RowBox[List["2", " ", "a", " ", "k"]], "+", RowBox[List["a", " ", "m"]]]], ")"]], " ", SuperscriptBox["z", "r"]]]]], "]"]]]]]], ")"]]]]]]]], "+", RowBox[List[RowBox[List["Binomial", "[", RowBox[List["m", ",", FractionBox["m", "2"]]], "]"]], " ", RowBox[List["(", RowBox[List["1", "-", RowBox[List["Mod", "[", RowBox[List["m", ",", "2"]], "]"]]]], ")"]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["s", "=", "0"]], RowBox[List["Floor", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "v"]], ")"]]]], "]"]]], RowBox[List[RowBox[List["Binomial", "[", RowBox[List["v", ",", "s"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["e", "-", RowBox[List["2", " ", "g", " ", "s"]], "+", RowBox[List["g", " ", "v"]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "b"]], "+", RowBox[List["2", " ", "c", " ", "s"]], "-", RowBox[List["c", " ", "v"]]]], ")"]], " ", SuperscriptBox["z", "r"]]], ")"]], RowBox[List["-", FractionBox["\[Alpha]", "r"]]]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["\[Alpha]", "r"], ",", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "b"]], "+", RowBox[List["2", " ", "c", " ", "s"]], "-", RowBox[List["c", " ", "v"]]]], ")"]], " ", SuperscriptBox["z", "r"]]]]], "]"]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["e", "+", RowBox[List["2", " ", "g", " ", "s"]], "-", RowBox[List["g", " ", "v"]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "b"]], "-", RowBox[List["2", " ", "c", " ", "s"]], "+", RowBox[List["c", " ", "v"]]]], ")"]], " ", SuperscriptBox["z", "r"]]], ")"]], RowBox[List["-", FractionBox["\[Alpha]", "r"]]]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["\[Alpha]", "r"], ",", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "b"]], "-", RowBox[List["2", " ", "c", " ", "s"]], "+", RowBox[List["c", " ", "v"]]]], ")"]], " ", SuperscriptBox["z", "r"]]]]], "]"]]]]]], ")"]]]]]]]], "+", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], RowBox[List["Floor", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "m"]], ")"]]]], "]"]]], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "k"], " ", RowBox[List["Binomial", "[", RowBox[List["m", ",", "k"]], "]"]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["s", "=", "0"]], RowBox[List["Floor", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "v"]], ")"]]]], "]"]]], RowBox[List[RowBox[List["Binomial", "[", RowBox[List["v", ",", "s"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["e", "-", FractionBox[RowBox[List["\[ImaginaryI]", " ", "m", " ", "\[Pi]"]], "2"], "-", RowBox[List["2", " ", "k", " ", "q"]], "+", RowBox[List["m", " ", "q"]], "-", RowBox[List["2", " ", "g", " ", "s"]], "+", RowBox[List["g", " ", "v"]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "b"]], "+", RowBox[List["2", " ", "a", " ", "k"]], "-", RowBox[List["a", " ", "m"]], "+", RowBox[List["2", " ", "c", " ", "s"]], "-", RowBox[List["c", " ", "v"]]]], ")"]], " ", SuperscriptBox["z", "r"]]], ")"]], RowBox[List["-", FractionBox["\[Alpha]", "r"]]]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["\[Alpha]", "r"], ",", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "b"]], "+", RowBox[List["2", " ", "a", " ", "k"]], "-", RowBox[List["a", " ", "m"]], "+", RowBox[List["2", " ", "c", " ", "s"]], "-", RowBox[List["c", " ", "v"]]]], ")"]], " ", SuperscriptBox["z", "r"]]]]], "]"]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["e", "+", FractionBox[RowBox[List["\[ImaginaryI]", " ", "m", " ", "\[Pi]"]], "2"], "+", RowBox[List["2", " ", "k", " ", "q"]], "-", RowBox[List["m", " ", "q"]], "-", RowBox[List["2", " ", "g", " ", "s"]], "+", RowBox[List["g", " ", "v"]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "b"]], "-", RowBox[List["2", " ", "a", " ", "k"]], "+", RowBox[List["a", " ", "m"]], "+", RowBox[List["2", " ", "c", " ", "s"]], "-", RowBox[List["c", " ", "v"]]]], ")"]], " ", SuperscriptBox["z", "r"]]], ")"]], RowBox[List["-", FractionBox["\[Alpha]", "r"]]]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["\[Alpha]", "r"], ",", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "b"]], "-", RowBox[List["2", " ", "a", " ", "k"]], "+", RowBox[List["a", " ", "m"]], "+", RowBox[List["2", " ", "c", " ", "s"]], "-", RowBox[List["c", " ", "v"]]]], ")"]], " ", SuperscriptBox["z", "r"]]]]], "]"]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["e", "-", FractionBox[RowBox[List["\[ImaginaryI]", " ", "m", " ", "\[Pi]"]], "2"], "-", RowBox[List["2", " ", "k", " ", "q"]], "+", RowBox[List["m", " ", "q"]], "+", RowBox[List["2", " ", "g", " ", "s"]], "-", RowBox[List["g", " ", "v"]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "b"]], "+", RowBox[List["2", " ", "a", " ", "k"]], "-", RowBox[List["a", " ", "m"]], "-", RowBox[List["2", " ", "c", " ", "s"]], "+", RowBox[List["c", " ", "v"]]]], ")"]], " ", SuperscriptBox["z", "r"]]], ")"]], RowBox[List["-", FractionBox["\[Alpha]", "r"]]]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["\[Alpha]", "r"], ",", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "b"]], "+", RowBox[List["2", " ", "a", " ", "k"]], "-", RowBox[List["a", " ", "m"]], "-", RowBox[List["2", " ", "c", " ", "s"]], "+", RowBox[List["c", " ", "v"]]]], ")"]], " ", SuperscriptBox["z", "r"]]]]], "]"]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["e", "+", FractionBox[RowBox[List["\[ImaginaryI]", " ", "m", " ", "\[Pi]"]], "2"], "+", RowBox[List["2", " ", "k", " ", "q"]], "-", RowBox[List["m", " ", "q"]], "+", RowBox[List["2", " ", "g", " ", "s"]], "-", RowBox[List["g", " ", "v"]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "b"]], "-", RowBox[List["2", " ", "a", " ", "k"]], "+", RowBox[List["a", " ", "m"]], "-", RowBox[List["2", " ", "c", " ", "s"]], "+", RowBox[List["c", " ", "v"]]]], ")"]], " ", SuperscriptBox["z", "r"]]], ")"]], RowBox[List["-", FractionBox["\[Alpha]", "r"]]]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["\[Alpha]", "r"], ",", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "b"]], "-", RowBox[List["2", " ", "a", " ", "k"]], "+", RowBox[List["a", " ", "m"]], "-", RowBox[List["2", " ", "c", " ", "s"]], "+", RowBox[List["c", " ", "v"]]]], ")"]], " ", SuperscriptBox["z", "r"]]]]], "]"]]]]]], ")"]]]]]]]]]]]], ")"]]]], "r"]]], "/;", RowBox[List[RowBox[List["m", "\[Element]", "Integers"]], "&&", RowBox[List["m", ">", "0"]], "&&", RowBox[List["v", "\[Element]", "Integers"]], "&&", RowBox[List["v", ">", "0"]]]]]]]]]]










Date Added to functions.wolfram.com (modification date)





2002-12-18