Wolfram Researchfunctions.wolfram.comOther Wolfram Sites
Search Site
Function CategoriesGraphics GalleryNotationsGeneral IdentitiesAbout This Site ContributeEmail CommentsSign the Guestbook

View Related Information In
The Documentation Center
MathWorld

Download All Formulas For This Function
Mathematica Notebook
PDF File

 

Developed with Mathematica -- Download a Free Trial Version
 











variants of this functions
HypergeometricPFQRegularized






Mathematica Notation

Traditional Notation









Hypergeometric Functions > HypergeometricPFQRegularized[{a1,...,ap},{b1,...,bq},z] > Continued fraction representations





http://functions.wolfram.com/07.32.10.0001.01









  


  










Input Form





HypergeometricPFQRegularized[{Subscript[a, 1], \[Ellipsis], Subscript[a, p]}, {Subscript[b, 1], \[Ellipsis], Subscript[b, q]}, z] == (1/Product[Gamma[Subscript[b, k]], {k, 1, q}]) (1 + (z Product[Subscript[a, k]/Product[Subscript[b, k], {k, 1, q}], {k, 1, p}])/(1 + -((z Product[1 + Subscript[a, j], {j, 1, p}])/ (2 Product[1 + Subscript[b, j], {j, 1, q}]))/ (1 + (z Product[1 + Subscript[a, j], {j, 1, p}])/ (2 Product[1 + Subscript[b, j], {j, 1, q}]) - (z Product[2 + Subscript[a, j], {j, 1, p}])/ (3 Product[2 + Subscript[b, j], {j, 1, q}])/ (1 + (z Product[2 + Subscript[a, j], {j, 1, p}])/ (3 Product[2 + Subscript[b, j], {j, 1, q}]) + \[Ellipsis]))))










Standard Form





Cell[BoxData[RowBox[List[RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["a", "1"], ",", "\[Ellipsis]", ",", SubscriptBox["a", "p"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["b", "1"], ",", "\[Ellipsis]", ",", SubscriptBox["b", "q"]]], "}"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox[RowBox[List[" ", "1"]], RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["k", "=", "1"]], "q"], RowBox[List["Gamma", "[", SubscriptBox["b", "k"], "]"]]]]], RowBox[List["(", RowBox[List["1", "+", RowBox[List[RowBox[List["(", RowBox[List["z", RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["k", "=", "1"]], "p"], RowBox[List[SubscriptBox["a", "k"], "/", RowBox[List["(", " ", RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["k", "=", "1"]], "q"], SubscriptBox["b", "k"]]], ")"]]]]]]]], ")"]], "/", RowBox[List["(", RowBox[List["1", "+", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["z", " ", RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["j", "=", "1"]], "p"], RowBox[List["(", RowBox[List["1", "+", SubscriptBox["a", "j"]]], ")"]]]]]], RowBox[List["2", " ", RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["j", "=", "1"]], "q"], RowBox[List["(", RowBox[List["1", "+", SubscriptBox["b", "j"]]], ")"]]]]]]]]], "/", RowBox[List["(", RowBox[List["1", "+", FractionBox[RowBox[List["z", " ", RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["j", "=", "1"]], "p"], RowBox[List["(", RowBox[List["1", "+", SubscriptBox["a", "j"]]], ")"]]]]]], RowBox[List["2", " ", RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["j", "=", "1"]], "q"], RowBox[List["(", RowBox[List["1", "+", SubscriptBox["b", "j"]]], ")"]]]]]]], "+", FractionBox[RowBox[List["-", FractionBox[RowBox[List["z", " ", RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["j", "=", "1"]], "p"], RowBox[List["(", RowBox[List["2", "+", SubscriptBox["a", "j"]]], ")"]]]]]], RowBox[List["3", " ", RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["j", "=", "1"]], "q"], RowBox[List["(", RowBox[List["2", "+", SubscriptBox["b", "j"]]], ")"]]]]]]]]], RowBox[List["1", "+", FractionBox[RowBox[List["z", " ", RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["j", "=", "1"]], "p"], RowBox[List["(", RowBox[List["2", "+", SubscriptBox["a", "j"]]], ")"]]]]]], RowBox[List["3", " ", RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["j", "=", "1"]], "q"], RowBox[List["(", RowBox[List["2", "+", SubscriptBox["b", "j"]]], ")"]]]]]]], "+", "\[Ellipsis]"]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]]]]










MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <semantics> <mrow> <mrow> <msub> <mo> &#8202; </mo> <mi> p </mi> </msub> <msub> <mover> <mi> F </mi> <mo> ~ </mo> </mover> <mi> q </mi> </msub> </mrow> <mo> &#8289; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msub> <mi> a </mi> <mn> 1 </mn> </msub> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <msub> <mi> a </mi> <mi> p </mi> </msub> </mrow> <mo> ; </mo> <mrow> <msub> <mi> b </mi> <mn> 1 </mn> </msub> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <msub> <mi> b </mi> <mi> q </mi> </msub> </mrow> <mo> ; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[RowBox[List[SubscriptBox[&quot;\[InvisiblePrefixScriptBase]&quot;, &quot;p&quot;], SubscriptBox[OverscriptBox[&quot;F&quot;, &quot;~&quot;], FormBox[&quot;q&quot;, TraditionalForm]]]], &quot;\[InvisibleApplication]&quot;, RowBox[List[&quot;(&quot;, RowBox[List[TagBox[TagBox[RowBox[List[TagBox[SubscriptBox[&quot;a&quot;, &quot;1&quot;], HypergeometricPFQ, Rule[Editable, True]], &quot;,&quot;, TagBox[&quot;\[Ellipsis]&quot;, HypergeometricPFQ, Rule[Editable, True]], &quot;,&quot;, TagBox[SubscriptBox[&quot;a&quot;, &quot;p&quot;], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, True]], &quot;;&quot;, TagBox[TagBox[RowBox[List[TagBox[SubscriptBox[&quot;b&quot;, &quot;1&quot;], HypergeometricPFQ, Rule[Editable, True]], &quot;,&quot;, TagBox[&quot;\[Ellipsis]&quot;, HypergeometricPFQ, Rule[Editable, True]], &quot;,&quot;, TagBox[SubscriptBox[&quot;b&quot;, &quot;q&quot;], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, True]], &quot;;&quot;, &quot;z&quot;]], &quot;)&quot;]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, True]] </annotation> </semantics> <mo> &#10869; </mo> <mrow> <mfrac> <mn> 1 </mn> <mrow> <munderover> <mo> &#8719; </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> q </mi> </munderover> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <msub> <mi> b </mi> <mi> k </mi> </msub> <mo> ) </mo> </mrow> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> &#8290; </mo> <mrow> <munderover> <mo> &#8719; </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> p </mi> </munderover> <mrow> <msub> <mi> a </mi> <mi> k </mi> </msub> <mo> / </mo> <mrow> <mo> ( </mo> <mtext> </mtext> <mrow> <munderover> <mo> &#8719; </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> q </mi> </munderover> <msub> <mi> b </mi> <mi> k </mi> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> / </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <mstyle scriptlevel='0'> <mrow> <mrow> <mo> - </mo> <mfrac> <mrow> <mi> z </mi> <mo> &#8290; </mo> <mrow> <munderover> <mo> &#8719; </mo> <mrow> <mi> j </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> p </mi> </munderover> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <msub> <mi> a </mi> <mi> j </mi> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <munderover> <mo> &#8719; </mo> <mrow> <mi> j </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> q </mi> </munderover> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <msub> <mi> b </mi> <mi> j </mi> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mfrac> </mrow> <mo> / </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <mfrac> <mrow> <mi> z </mi> <mo> &#8290; </mo> <mrow> <munderover> <mo> &#8719; </mo> <mrow> <mi> j </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> p </mi> </munderover> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <msub> <mi> a </mi> <mi> j </mi> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <munderover> <mo> &#8719; </mo> <mrow> <mi> j </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> q </mi> </munderover> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <msub> <mi> b </mi> <mi> j </mi> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mfrac> <mo> + </mo> <mfrac> <mrow> <mo> - </mo> <mfrac> <mrow> <mi> z </mi> <mo> &#8290; </mo> <mrow> <munderover> <mo> &#8719; </mo> <mrow> <mi> j </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> p </mi> </munderover> <mrow> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> + </mo> <msub> <mi> a </mi> <mi> j </mi> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <mrow> <munderover> <mo> &#8719; </mo> <mrow> <mi> j </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> q </mi> </munderover> <mrow> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> + </mo> <msub> <mi> b </mi> <mi> j </mi> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mfrac> </mrow> <mstyle scriptlevel='0'> <mrow> <mn> 1 </mn> <mo> + </mo> <mfrac> <mrow> <mi> z </mi> <mo> &#8290; </mo> <mrow> <munderover> <mo> &#8719; </mo> <mrow> <mi> j </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> p </mi> </munderover> <mrow> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> + </mo> <msub> <mi> a </mi> <mi> j </mi> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <mrow> <munderover> <mo> &#8719; </mo> <mrow> <mi> j </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> q </mi> </munderover> <mrow> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> + </mo> <msub> <mi> b </mi> <mi> j </mi> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mfrac> <mo> + </mo> <mo> &#8230; </mo> </mrow> </mstyle> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> </mstyle> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <mrow> <semantics> <mrow> <mrow> <msub> <mo> &#8202; </mo> <mi> p </mi> </msub> <msub> <mover> <mi> F </mi> <mo> ~ </mo> </mover> <mi> q </mi> </msub> </mrow> <mo> &#8289; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msub> <mi> a </mi> <mn> 1 </mn> </msub> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <msub> <mi> a </mi> <mi> p </mi> </msub> </mrow> <mo> ; </mo> <mrow> <msub> <mi> b </mi> <mn> 1 </mn> </msub> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <msub> <mi> b </mi> <mi> q </mi> </msub> </mrow> <mo> ; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[RowBox[List[SubscriptBox[&quot;\[InvisiblePrefixScriptBase]&quot;, &quot;p&quot;], SubscriptBox[OverscriptBox[&quot;F&quot;, &quot;~&quot;], FormBox[&quot;q&quot;, TraditionalForm]]]], &quot;\[InvisibleApplication]&quot;, RowBox[List[&quot;(&quot;, RowBox[List[TagBox[TagBox[RowBox[List[TagBox[SubscriptBox[&quot;a&quot;, &quot;1&quot;], HypergeometricPFQ, Rule[Editable, True]], &quot;,&quot;, TagBox[&quot;\[Ellipsis]&quot;, HypergeometricPFQ, Rule[Editable, True]], &quot;,&quot;, TagBox[SubscriptBox[&quot;a&quot;, &quot;p&quot;], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, True]], &quot;;&quot;, TagBox[TagBox[RowBox[List[TagBox[SubscriptBox[&quot;b&quot;, &quot;1&quot;], HypergeometricPFQ, Rule[Editable, True]], &quot;,&quot;, TagBox[&quot;\[Ellipsis]&quot;, HypergeometricPFQ, Rule[Editable, True]], &quot;,&quot;, TagBox[SubscriptBox[&quot;b&quot;, &quot;q&quot;], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, True]], &quot;;&quot;, &quot;z&quot;]], &quot;)&quot;]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, True]] </annotation> </semantics> <mo> &#10869; </mo> <mrow> <mfrac> <mn> 1 </mn> <mrow> <munderover> <mo> &#8719; </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> q </mi> </munderover> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <msub> <mi> b </mi> <mi> k </mi> </msub> <mo> ) </mo> </mrow> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> &#8290; </mo> <mrow> <munderover> <mo> &#8719; </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> p </mi> </munderover> <mrow> <msub> <mi> a </mi> <mi> k </mi> </msub> <mo> / </mo> <mrow> <mo> ( </mo> <mtext> </mtext> <mrow> <munderover> <mo> &#8719; </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> q </mi> </munderover> <msub> <mi> b </mi> <mi> k </mi> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> / </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <mstyle scriptlevel='0'> <mrow> <mrow> <mo> - </mo> <mfrac> <mrow> <mi> z </mi> <mo> &#8290; </mo> <mrow> <munderover> <mo> &#8719; </mo> <mrow> <mi> j </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> p </mi> </munderover> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <msub> <mi> a </mi> <mi> j </mi> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <munderover> <mo> &#8719; </mo> <mrow> <mi> j </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> q </mi> </munderover> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <msub> <mi> b </mi> <mi> j </mi> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mfrac> </mrow> <mo> / </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <mfrac> <mrow> <mi> z </mi> <mo> &#8290; </mo> <mrow> <munderover> <mo> &#8719; </mo> <mrow> <mi> j </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> p </mi> </munderover> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <msub> <mi> a </mi> <mi> j </mi> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <munderover> <mo> &#8719; </mo> <mrow> <mi> j </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> q </mi> </munderover> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <msub> <mi> b </mi> <mi> j </mi> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mfrac> <mo> + </mo> <mfrac> <mrow> <mo> - </mo> <mfrac> <mrow> <mi> z </mi> <mo> &#8290; </mo> <mrow> <munderover> <mo> &#8719; </mo> <mrow> <mi> j </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> p </mi> </munderover> <mrow> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> + </mo> <msub> <mi> a </mi> <mi> j </mi> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <mrow> <munderover> <mo> &#8719; </mo> <mrow> <mi> j </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> q </mi> </munderover> <mrow> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> + </mo> <msub> <mi> b </mi> <mi> j </mi> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mfrac> </mrow> <mstyle scriptlevel='0'> <mrow> <mn> 1 </mn> <mo> + </mo> <mfrac> <mrow> <mi> z </mi> <mo> &#8290; </mo> <mrow> <munderover> <mo> &#8719; </mo> <mrow> <mi> j </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> p </mi> </munderover> <mrow> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> + </mo> <msub> <mi> a </mi> <mi> j </mi> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <mrow> <munderover> <mo> &#8719; </mo> <mrow> <mi> j </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> q </mi> </munderover> <mrow> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> + </mo> <msub> <mi> b </mi> <mi> j </mi> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mfrac> <mo> + </mo> <mo> &#8230; </mo> </mrow> </mstyle> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> </mstyle> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["a_", "1"], ",", "\[Ellipsis]_", ",", SubscriptBox["a_", "p_"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["b_", "1"], ",", "\[Ellipsis]_", ",", SubscriptBox["b_", "q_"]]], "}"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["1", "+", FractionBox[RowBox[List["z", " ", RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["k", "=", "1"]], "p"], FractionBox[SubscriptBox["a", "k"], RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["k", "=", "1"]], "q"], SubscriptBox["b", "k"]]]]]]]], RowBox[List["1", "-", FractionBox[RowBox[List["z", " ", RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["j", "=", "1"]], "p"], RowBox[List["(", RowBox[List["1", "+", SubscriptBox["a", "j"]]], ")"]]]]]], RowBox[List[RowBox[List["(", RowBox[List["2", " ", RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["j", "=", "1"]], "q"], RowBox[List["(", RowBox[List["1", "+", SubscriptBox["b", "j"]]], ")"]]]]]], ")"]], " ", RowBox[List["(", RowBox[List["1", "+", FractionBox[RowBox[List["z", " ", RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["j", "=", "1"]], "p"], RowBox[List["(", RowBox[List["1", "+", SubscriptBox["a", "j"]]], ")"]]]]]], RowBox[List["2", " ", RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["j", "=", "1"]], "q"], RowBox[List["(", RowBox[List["1", "+", SubscriptBox["b", "j"]]], ")"]]]]]]], "-", FractionBox[RowBox[List["z", " ", RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["j", "=", "1"]], "p"], RowBox[List["(", RowBox[List["2", "+", SubscriptBox["a", "j"]]], ")"]]]]]], RowBox[List[RowBox[List["(", RowBox[List["3", " ", RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["j", "=", "1"]], "q"], RowBox[List["(", RowBox[List["2", "+", SubscriptBox["b", "j"]]], ")"]]]]]], ")"]], " ", RowBox[List["(", RowBox[List["1", "+", FractionBox[RowBox[List["z", " ", RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["j", "=", "1"]], "p"], RowBox[List["(", RowBox[List["2", "+", SubscriptBox["a", "j"]]], ")"]]]]]], RowBox[List["3", " ", RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["j", "=", "1"]], "q"], RowBox[List["(", RowBox[List["2", "+", SubscriptBox["b", "j"]]], ")"]]]]]]], "+", "\[Ellipsis]"]], ")"]]]]]]], ")"]]]]]]]]]], RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["k", "=", "1"]], "q"], RowBox[List["Gamma", "[", SubscriptBox["b", "k"], "]"]]]]]]]]]










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





2001-10-29





© 1998-2014 Wolfram Research, Inc.