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Csch






Mathematica Notation

Traditional Notation









Elementary Functions > Csch[z] > Integration > Indefinite integration > Involving functions of the direct function, hyperbolic, exponential, trigonometric and a power functions > Involving powers of the direct function, hyperbolic, exponential, trigonometric and a power functions > Involving sin, sinh, exp and power > Involving zn ep z sin(a z)sinh(b z) cschnu( c z)





http://functions.wolfram.com/01.23.21.0579.01









  


  










Input Form





Integrate[z^n E^(p z) Sin[a z] Sinh[b z] Csch[c z]^\[Nu], z] == (I/4) (1 - E^(2 c z))^\[Nu] Csch[c z]^\[Nu] n! ((-E^(((-I) a - b + p) z)) Sum[(((-1)^j z^(-j + n) ((-I) a - b + p + c \[Nu])^(-1 - j))/(-j + n)!) HypergeometricPFQ[{Subscript[a, 1], \[Ellipsis], Subscript[a, j + 1], \[Nu]}, {1 + Subscript[a, 1], \[Ellipsis], 1 + Subscript[a, j + 1]}, E^(2 c z)], {j, 0, n}] - E^((I a + b + p) z) Sum[(((-1)^j z^(-j + n) (I a + b + p + c \[Nu])^(-1 - j))/(-j + n)!) HypergeometricPFQ[{Subscript[b, 1], \[Ellipsis], Subscript[b, j + 1], \[Nu]}, {1 + Subscript[b, 1], \[Ellipsis], 1 + Subscript[b, j + 1]}, E^(2 c z)], {j, 0, n}] + E^((I a - b + p) z) Sum[(((-1)^j z^(-j + n) (I a - b + p + c \[Nu])^(-1 - j))/(-j + n)!) HypergeometricPFQ[{Subscript[c, 1], \[Ellipsis], Subscript[c, j + 1], \[Nu]}, {1 + Subscript[c, 1], \[Ellipsis], 1 + Subscript[c, j + 1]}, E^(2 c z)], {j, 0, n}] + E^(((-I) a + b + p) z) Sum[(((-1)^j z^(-j + n) ((-I) a + b + p + c \[Nu])^(-1 - j))/(-j + n)!) HypergeometricPFQ[{Subscript[d, 1], \[Ellipsis], Subscript[d, j + 1], \[Nu]}, {1 + Subscript[d, 1], \[Ellipsis], 1 + Subscript[d, j + 1]}, E^(2 c z)], {j, 0, n}]) /; Subscript[a, 1] == Subscript[a, 2] == \[Ellipsis] == Subscript[a, n + 1] == ((-I) a - b + p + c \[Nu])/(2 c) && Subscript[b, 1] == Subscript[b, 2] == \[Ellipsis] == Subscript[b, n + 1] == (I a + b + p + c \[Nu])/(2 c) && Subscript[c, 1] == Subscript[c, 2] == \[Ellipsis] == Subscript[c, n + 1] == (I a - b + p + c \[Nu])/(2 c) && Subscript[d, 1] == Subscript[d, 2] == \[Ellipsis] == Subscript[d, n + 1] == ((-I) a + b + p + c \[Nu])/(2 c) && Element[n, Integers] && n >= 0










Standard Form





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MathML Form







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</mo> <mrow> <mi> j </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mi> n </mi> </munderover> <mrow> <mfrac> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> j </mi> </msup> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mi> n </mi> <mo> - </mo> <mi> j </mi> </mrow> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> + </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> a </mi> </mrow> <mtext> </mtext> <mo> + </mo> <mi> p </mi> <mo> + </mo> <mrow> <mi> c </mi> <mo> &#8290; </mo> <mi> &#957; </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mrow> <mrow> <mo> - </mo> <mi> j </mi> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> </mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> n </mi> <mo> - </mo> <mi> j </mi> </mrow> <mo> ) </mo> </mrow> <mo> ! </mo> </mrow> </mfrac> <mo> &#8290; </mo> <semantics> <mrow> <mrow> <msub> <mo> &#8202; </mo> <mrow> <mi> j </mi> <mo> + </mo> <mn> 2 </mn> </mrow> </msub> <msub> <mi> F </mi> <mrow> <mi> j </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msub> </mrow> <mo> &#8289; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mfrac> <mrow> <mrow> <mi> c </mi> <mo> &#8290; </mo> <mi> &#957; </mi> </mrow> <mo> + </mo> <mi> p </mi> <mo> + </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> a </mi> </mrow> <mo> + </mo> <mi> b </mi> </mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> c </mi> </mrow> </mfrac> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <mfrac> <mrow> <mrow> <mi> c </mi> <mo> &#8290; </mo> <mi> &#957; </mi> </mrow> <mo> + </mo> <mi> p </mi> <mo> + </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> a </mi> </mrow> <mo> + </mo> <mi> b </mi> </mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> c </mi> </mrow> </mfrac> <mo> , </mo> <mi> &#957; </mi> </mrow> <mo> ; </mo> <mrow> <mrow> <mfrac> <mrow> <mrow> <mi> c </mi> <mo> &#8290; </mo> <mi> &#957; </mi> </mrow> <mo> + </mo> <mi> p </mi> <mo> + </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> a </mi> </mrow> <mo> + </mo> <mi> b </mi> </mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> c </mi> </mrow> </mfrac> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <mrow> <mfrac> <mrow> <mrow> <mi> c </mi> <mo> &#8290; </mo> <mi> &#957; </mi> </mrow> <mo> + </mo> <mi> p </mi> <mo> + </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> a </mi> </mrow> <mo> + </mo> <mi> b </mi> </mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> c </mi> </mrow> </mfrac> <mo> + </mo> <mn> 1 </mn> </mrow> </mrow> <mo> ; </mo> <msup> <mi> &#8519; </mi> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> c </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> </msup> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox[&quot;\[InvisiblePrefixScriptBase]&quot;, FormBox[RowBox[List[&quot;j&quot;, &quot;+&quot;, &quot;2&quot;]], TraditionalForm]], SubscriptBox[&quot;F&quot;, FormBox[RowBox[List[&quot;j&quot;, &quot;+&quot;, &quot;1&quot;]], TraditionalForm]]]], &quot;\[InvisibleApplication]&quot;, RowBox[List[&quot;(&quot;, RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox[RowBox[List[RowBox[List[&quot;c&quot;, &quot; &quot;, &quot;\[Nu]&quot;]], &quot;+&quot;, &quot;p&quot;, &quot;+&quot;, RowBox[List[&quot;\[ImaginaryI]&quot;, &quot; &quot;, &quot;a&quot;]], &quot;+&quot;, &quot;b&quot;]], RowBox[List[&quot;2&quot;, &quot; &quot;, &quot;c&quot;]]], HypergeometricPFQ], &quot;,&quot;, TagBox[&quot;\[Ellipsis]&quot;, HypergeometricPFQ], &quot;,&quot;, TagBox[FractionBox[RowBox[List[RowBox[List[&quot;c&quot;, &quot; &quot;, &quot;\[Nu]&quot;]], &quot;+&quot;, &quot;p&quot;, &quot;+&quot;, RowBox[List[&quot;\[ImaginaryI]&quot;, &quot; &quot;, &quot;a&quot;]], &quot;+&quot;, &quot;b&quot;]], RowBox[List[&quot;2&quot;, &quot; &quot;, &quot;c&quot;]]], HypergeometricPFQ], &quot;,&quot;, TagBox[&quot;\[Nu]&quot;, HypergeometricPFQ]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ], &quot;;&quot;, TagBox[TagBox[RowBox[List[TagBox[RowBox[List[FractionBox[RowBox[List[RowBox[List[&quot;c&quot;, &quot; &quot;, &quot;\[Nu]&quot;]], &quot;+&quot;, &quot;p&quot;, &quot;+&quot;, RowBox[List[&quot;\[ImaginaryI]&quot;, &quot; &quot;, &quot;a&quot;]], &quot;+&quot;, &quot;b&quot;]], RowBox[List[&quot;2&quot;, &quot; &quot;, &quot;c&quot;]]], &quot;+&quot;, &quot;1&quot;]], HypergeometricPFQ], &quot;,&quot;, TagBox[&quot;\[Ellipsis]&quot;, HypergeometricPFQ], &quot;,&quot;, TagBox[RowBox[List[FractionBox[RowBox[List[RowBox[List[&quot;c&quot;, &quot; &quot;, &quot;\[Nu]&quot;]], &quot;+&quot;, &quot;p&quot;, &quot;+&quot;, RowBox[List[&quot;\[ImaginaryI]&quot;, &quot; &quot;, &quot;a&quot;]], &quot;+&quot;, &quot;b&quot;]], RowBox[List[&quot;2&quot;, &quot; &quot;, &quot;c&quot;]]], &quot;+&quot;, &quot;1&quot;]], HypergeometricPFQ]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ], &quot;;&quot;, TagBox[SuperscriptBox[&quot;\[ExponentialE]&quot;, RowBox[List[&quot;2&quot;, &quot; &quot;, &quot;c&quot;, &quot; &quot;, &quot;z&quot;]]], HypergeometricPFQ]]], &quot;)&quot;]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]]], HypergeometricPFQ] </annotation> </semantics> </mrow> </mrow> </mrow> <mo> + </mo> <mrow> <msup> <mi> &#8519; </mi> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> a </mi> </mrow> <mo> - </mo> <mi> b </mi> <mo> + </mo> <mi> p </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> </msup> <mo> &#8290; </mo> <mtext> </mtext> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <mi> j </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mi> n </mi> </munderover> <mrow> <mfrac> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> j </mi> </msup> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mi> n </mi> <mo> - </mo> <mi> j </mi> </mrow> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> a </mi> </mrow> <mo> - </mo> <mi> b </mi> <mo> + </mo> <mi> p </mi> <mo> + </mo> <mrow> <mi> c </mi> <mo> &#8290; </mo> <mi> &#957; </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mrow> <mrow> <mo> - </mo> <mi> j </mi> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> </mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> n </mi> <mo> - </mo> <mi> j </mi> </mrow> <mo> ) </mo> </mrow> <mo> ! </mo> </mrow> </mfrac> <mo> &#8290; </mo> <semantics> <mrow> <mrow> <msub> <mo> &#8202; </mo> <mrow> <mi> j </mi> <mo> + </mo> <mn> 2 </mn> </mrow> </msub> <msub> <mi> F </mi> <mrow> <mi> j </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msub> </mrow> <mo> &#8289; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mfrac> <mrow> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> a </mi> </mrow> <mo> - </mo> <mi> b </mi> <mo> + </mo> <mi> p </mi> <mo> + </mo> <mrow> <mi> c </mi> <mo> &#8290; </mo> <mi> &#957; </mi> </mrow> </mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> c </mi> </mrow> </mfrac> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <mfrac> <mrow> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> a </mi> </mrow> <mo> - </mo> <mi> b </mi> <mo> + </mo> <mi> p </mi> <mo> + </mo> <mrow> <mi> c </mi> <mo> &#8290; </mo> <mi> &#957; </mi> </mrow> </mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> c </mi> </mrow> </mfrac> <mo> , </mo> <mi> &#957; </mi> </mrow> <mo> ; </mo> <mrow> <mrow> <mfrac> <mrow> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> a </mi> </mrow> <mo> - </mo> <mi> b </mi> <mo> + </mo> <mi> p </mi> <mo> + </mo> <mrow> <mi> c </mi> <mo> &#8290; </mo> <mi> &#957; </mi> </mrow> </mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> c </mi> </mrow> </mfrac> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <mrow> <mfrac> <mrow> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> a </mi> </mrow> <mo> - </mo> <mi> b </mi> <mo> + </mo> <mi> p </mi> <mo> + </mo> <mrow> <mi> c </mi> <mo> &#8290; </mo> <mi> &#957; </mi> </mrow> </mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> c </mi> </mrow> </mfrac> <mo> + </mo> <mn> 1 </mn> </mrow> </mrow> <mo> ; </mo> <msup> <mi> &#8519; </mi> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> c </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> </msup> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox[&quot;\[InvisiblePrefixScriptBase]&quot;, FormBox[RowBox[List[&quot;j&quot;, &quot;+&quot;, &quot;2&quot;]], TraditionalForm]], SubscriptBox[&quot;F&quot;, FormBox[RowBox[List[&quot;j&quot;, &quot;+&quot;, &quot;1&quot;]], TraditionalForm]]]], &quot;\[InvisibleApplication]&quot;, RowBox[List[&quot;(&quot;, RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox[RowBox[List[RowBox[List[&quot;\[ImaginaryI]&quot;, &quot; 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&quot;, &quot;\[Nu]&quot;]]]], RowBox[List[&quot;2&quot;, &quot; &quot;, &quot;c&quot;]]], &quot;+&quot;, &quot;1&quot;]], HypergeometricPFQ], &quot;,&quot;, TagBox[&quot;\[Ellipsis]&quot;, HypergeometricPFQ], &quot;,&quot;, TagBox[RowBox[List[FractionBox[RowBox[List[RowBox[List[&quot;\[ImaginaryI]&quot;, &quot; &quot;, &quot;a&quot;]], &quot;-&quot;, &quot;b&quot;, &quot;+&quot;, &quot;p&quot;, &quot;+&quot;, RowBox[List[&quot;c&quot;, &quot; &quot;, &quot;\[Nu]&quot;]]]], RowBox[List[&quot;2&quot;, &quot; &quot;, &quot;c&quot;]]], &quot;+&quot;, &quot;1&quot;]], HypergeometricPFQ]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ], &quot;;&quot;, TagBox[SuperscriptBox[&quot;\[ExponentialE]&quot;, RowBox[List[&quot;2&quot;, &quot; &quot;, &quot;c&quot;, &quot; &quot;, &quot;z&quot;]]], HypergeometricPFQ]]], &quot;)&quot;]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]]], HypergeometricPFQ] </annotation> </semantics> </mrow> </mrow> </mrow> <mo> + </mo> <mrow> <msup> <mi> &#8519; </mi> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mi> &#8520; </mi> </mrow> <mo> &#8290; </mo> <mi> a </mi> </mrow> <mo> + </mo> <mi> b </mi> <mo> + </mo> <mi> p </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> </msup> <mo> &#8290; </mo> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <mi> j </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mi> n </mi> </munderover> <mrow> <mfrac> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> j </mi> </msup> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mi> n </mi> <mo> - </mo> <mi> j </mi> </mrow> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mi> &#8520; </mi> </mrow> <mo> &#8290; </mo> <mi> a </mi> </mrow> <mo> + </mo> <mi> b </mi> <mo> + </mo> <mi> p </mi> <mo> + </mo> <mrow> <mi> c </mi> <mo> &#8290; </mo> <mi> &#957; </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mrow> <mrow> <mo> - </mo> <mi> j </mi> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> </mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> n </mi> <mo> - </mo> <mi> j </mi> </mrow> <mo> ) </mo> </mrow> <mo> ! </mo> </mrow> </mfrac> <mo> &#8290; </mo> <semantics> <mrow> <mrow> <msub> <mo> &#8202; </mo> <mrow> <mi> j </mi> <mo> + </mo> <mn> 2 </mn> </mrow> </msub> <msub> <mi> F </mi> <mrow> <mi> j </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msub> </mrow> <mo> &#8289; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mfrac> <mrow> <mrow> <mrow> <mo> - </mo> <mi> &#8520; </mi> </mrow> <mo> &#8290; </mo> <mi> a </mi> </mrow> <mo> + </mo> <mi> b </mi> <mo> + </mo> <mi> p </mi> <mo> + </mo> <mrow> <mi> c </mi> <mo> &#8290; </mo> <mi> &#957; </mi> </mrow> </mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> c </mi> </mrow> </mfrac> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <mfrac> <mrow> <mrow> <mrow> <mo> - </mo> <mi> &#8520; </mi> </mrow> <mo> &#8290; </mo> <mi> a </mi> </mrow> <mo> + </mo> <mi> b </mi> <mo> + </mo> <mi> p </mi> <mo> + </mo> <mrow> <mi> c </mi> <mo> &#8290; </mo> <mi> &#957; </mi> </mrow> </mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> c </mi> </mrow> </mfrac> <mo> , </mo> <mi> &#957; </mi> </mrow> <mo> ; </mo> <mrow> <mrow> <mfrac> <mrow> <mrow> <mrow> <mo> - </mo> <mi> &#8520; </mi> </mrow> <mo> &#8290; </mo> <mi> a </mi> </mrow> <mo> + </mo> <mi> b </mi> <mo> + </mo> <mi> p </mi> <mo> + </mo> <mrow> <mi> c </mi> <mo> &#8290; </mo> <mi> &#957; </mi> </mrow> </mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> c </mi> </mrow> </mfrac> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <mrow> <mfrac> <mrow> <mrow> <mrow> <mo> - </mo> <mi> &#8520; </mi> </mrow> <mo> &#8290; </mo> <mi> a </mi> </mrow> <mo> + </mo> <mi> b </mi> <mo> + </mo> <mi> p </mi> <mo> + </mo> <mrow> <mi> c </mi> <mo> &#8290; </mo> <mi> &#957; </mi> </mrow> </mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> c </mi> </mrow> </mfrac> <mo> + </mo> <mn> 1 </mn> </mrow> </mrow> <mo> ; </mo> <msup> <mi> &#8519; </mi> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> c </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> </msup> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox[&quot;\[InvisiblePrefixScriptBase]&quot;, FormBox[RowBox[List[&quot;j&quot;, &quot;+&quot;, &quot;2&quot;]], TraditionalForm]], SubscriptBox[&quot;F&quot;, FormBox[RowBox[List[&quot;j&quot;, &quot;+&quot;, &quot;1&quot;]], TraditionalForm]]]], &quot;\[InvisibleApplication]&quot;, RowBox[List[&quot;(&quot;, RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox[RowBox[List[RowBox[List[RowBox[List[&quot;-&quot;, &quot;\[ImaginaryI]&quot;]], &quot; 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</ci> </list> <list> <apply> <plus /> <apply> <times /> <apply> <plus /> <apply> <times /> <ci> c </ci> <ci> &#957; </ci> </apply> <ci> p </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> a </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> <ci> &#8230; </ci> <apply> <plus /> <apply> <times /> <apply> <plus /> <apply> <times /> <ci> c </ci> <ci> &#957; </ci> </apply> <ci> p </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> a </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> </list> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <apply> <plus /> <apply> <times /> <imaginaryi /> <ci> a </ci> </apply> <ci> b </ci> <ci> p </ci> </apply> <ci> z </ci> </apply> </apply> <apply> <sum /> <bvar> <ci> j </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <ci> n </ci> </uplimit> <apply> <times /> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <ci> j </ci> </apply> <apply> <power /> <ci> z </ci> <apply> <plus /> <ci> n </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> j </ci> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <ci> b </ci> <apply> <times /> <imaginaryi /> <ci> a </ci> </apply> <ci> p </ci> <apply> <times /> <ci> c </ci> <ci> &#957; </ci> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> j </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <apply> <factorial /> <apply> <plus /> <ci> n </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> j </ci> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> HypergeometricPFQ </ci> <list> <apply> <times /> <apply> <plus /> <apply> <times /> <ci> c </ci> <ci> &#957; </ci> </apply> <ci> p </ci> <apply> <times /> <imaginaryi /> <ci> a </ci> </apply> <ci> b </ci> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <ci> &#8230; </ci> <apply> <times /> <apply> <plus /> <apply> <times /> <ci> c </ci> <ci> &#957; </ci> </apply> <ci> p </ci> <apply> <times /> <imaginaryi /> <ci> a </ci> </apply> <ci> b </ci> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <ci> &#957; </ci> </list> <list> <apply> <plus /> <apply> <times /> <apply> <plus /> <apply> <times /> <ci> c </ci> <ci> &#957; </ci> </apply> <ci> p </ci> <apply> <times /> <imaginaryi /> <ci> a </ci> </apply> <ci> b </ci> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> <ci> &#8230; </ci> <apply> <plus /> <apply> <times /> <apply> <plus /> <apply> <times /> <ci> c </ci> <ci> &#957; </ci> </apply> <ci> p </ci> <apply> <times /> <imaginaryi /> <ci> a </ci> </apply> <ci> b </ci> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> </list> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <apply> <plus /> <apply> <times /> <imaginaryi /> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> <ci> p </ci> </apply> <ci> z </ci> </apply> </apply> <apply> <sum /> <bvar> <ci> j </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <ci> n </ci> </uplimit> <apply> <times /> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <ci> j </ci> </apply> <apply> <power /> <ci> z </ci> <apply> <plus /> <ci> n </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> j </ci> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <imaginaryi /> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> <ci> p </ci> <apply> <times /> <ci> c </ci> <ci> &#957; </ci> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> j </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <apply> <factorial /> <apply> <plus /> <ci> n </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> j </ci> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> HypergeometricPFQ </ci> <list> <apply> <times /> <apply> <plus /> <apply> <times /> <imaginaryi /> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> <ci> p </ci> <apply> <times /> <ci> c </ci> <ci> &#957; </ci> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <ci> &#8230; </ci> <apply> <times /> <apply> <plus /> <apply> <times /> <imaginaryi /> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> <ci> p </ci> <apply> <times /> <ci> c </ci> <ci> &#957; </ci> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <ci> &#957; </ci> </list> <list> <apply> <plus /> <apply> <times /> <apply> <plus /> <apply> <times /> <imaginaryi /> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> <ci> p </ci> <apply> <times /> <ci> c </ci> <ci> &#957; </ci> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> <ci> &#8230; </ci> <apply> <plus /> <apply> <times /> <apply> <plus /> <apply> <times /> <imaginaryi /> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> <ci> p </ci> <apply> <times /> <ci> c </ci> <ci> &#957; </ci> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> </list> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <apply> <plus /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <imaginaryi /> </apply> <ci> a </ci> </apply> <ci> b </ci> <ci> p </ci> </apply> <ci> z </ci> </apply> </apply> <apply> <sum /> <bvar> <ci> j </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <ci> n </ci> </uplimit> <apply> <times /> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <ci> j </ci> </apply> <apply> <power /> <ci> z </ci> <apply> <plus /> <ci> n </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> j </ci> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <imaginaryi /> </apply> <ci> a </ci> </apply> <ci> b </ci> <ci> p </ci> <apply> <times /> <ci> c </ci> <ci> &#957; 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Rule Form





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





2002-12-18