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| Hypergeometric Functions  HypergeometricPFQ[{a1,a2,a3},{b1,b2},z]  Specific values  For integer and half-integer parameters and fixed z  For fixed z and a1=-5/2, a2>=-5/2  For fixed z and a1=-5/2, a2=-1/2, a3>=-1/2  For fixed z and a1=-5/2, a2=-1/2, a3=3  For fixed z and a1=-5/2, a2=-1/2, a3=3, b1=3/2   |  |  
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 | | http://functions.wolfram.com/07.27.03.aa2a.01 | 
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 | | HypergeometricPFQ[{-(5/2), -(1/2), 3}, {3/2, 3/2}, z] == 
 (799 + 490 z - 105 z^2)/1024 - (15 (11 + 17 z - 35 z^2 + 7 z^3) 
    Log[1 - Sqrt[z]])/(2048 Sqrt[z]) + 
  (15 (11 + 17 z - 35 z^2 + 7 z^3) Log[1 + Sqrt[z]])/(2048 Sqrt[z]) - 
  (15 (1 + 15 z) PolyLog[2, -Sqrt[z]])/(512 Sqrt[z]) + 
  (15 (1 + 15 z) PolyLog[2, Sqrt[z]])/(512 Sqrt[z]) | 
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   <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>   </mo>  <mn> 3 </mn>  </msub>  <msub>  <mi> F </mi>  <mn> 2 </mn>  </msub>  </mrow>  <mo> ⁡ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mrow>  <mo> - </mo>  <mfrac>  <mn> 5 </mn>  <mn> 2 </mn>  </mfrac>  </mrow>  <mo> , </mo>  <mrow>  <mo> - </mo>  <mfrac>  <mn> 1 </mn>  <mn> 2 </mn>  </mfrac>  </mrow>  <mo> , </mo>  <mn> 3 </mn>  </mrow>  <mo> ; </mo>  <mrow>  <mfrac>  <mn> 3 </mn>  <mn> 2 </mn>  </mfrac>  <mo> , </mo>  <mfrac>  <mn> 3 </mn>  <mn> 2 </mn>  </mfrac>  </mrow>  <mo> ; </mo>  <mi> z </mi>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "3"], SubscriptBox["F", "2"]]], "\[InvisibleApplication]", RowBox[List["(", 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Rule[Editable, False], Rule[Selectable, False]], HypergeometricPFQ] </annotation>  </semantics>  <mo>  </mo>  <mrow>  <mfrac>  <mrow>  <mrow>  <mrow>  <mo> - </mo>  <mn> 105 </mn>  </mrow>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 2 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 490 </mn>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  <mo> + </mo>  <mn> 799 </mn>  </mrow>  <mn> 1024 </mn>  </mfrac>  <mo> - </mo>  <mfrac>  <mrow>  <mn> 15 </mn>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mn> 7 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 3 </mn>  </msup>  </mrow>  <mo> - </mo>  <mrow>  <mn> 35 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 2 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 17 </mn>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  <mo> + </mo>  <mn> 11 </mn>  </mrow>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <mrow>  <mi> log </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <mrow>  <mn> 1 </mn>  <mo> - </mo>  <msqrt>  <mi> z </mi>  </msqrt>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <mrow>  <mn> 2048 </mn>  <mo> ⁢ </mo>  <msqrt>  <mi> z </mi>  </msqrt>  </mrow>  </mfrac>  <mo> + </mo>  <mfrac>  <mrow>  <mn> 15 </mn>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mn> 7 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 3 </mn>  </msup>  </mrow>  <mo> - </mo>  <mrow>  <mn> 35 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 2 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 17 </mn>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  <mo> + </mo>  <mn> 11 </mn>  </mrow>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <mrow>  <mi> log </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <mrow>  <msqrt>  <mi> z </mi>  </msqrt>  <mo> + </mo>  <mn> 1 </mn>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <mrow>  <mn> 2048 </mn>  <mo> ⁢ </mo>  <msqrt>  <mi> z </mi>  </msqrt>  </mrow>  </mfrac>  <mo> - </mo>  <mfrac>  <mrow>  <mn> 15 </mn>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mn> 15 </mn>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  <mo> + </mo>  <mn> 1 </mn>  </mrow>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <mrow>  <msub>  <semantics>  <mi> Li </mi>  <annotation-xml encoding='MathML-Content'>  <ci> PolyLog </ci>  </annotation-xml>  </semantics>  <mn> 2 </mn>  </msub>  <mo> ( </mo>  <mrow>  <mo> - </mo>  <msqrt>  <mi> z </mi>  </msqrt>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <mrow>  <mn> 512 </mn>  <mo> ⁢ </mo>  <msqrt>  <mi> z </mi>  </msqrt>  </mrow>  </mfrac>  <mo> + </mo>  <mfrac>  <mrow>  <mn> 15 </mn>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mn> 15 </mn>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  <mo> + </mo>  <mn> 1 </mn>  </mrow>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <mrow>  <msub>  <semantics>  <mi> Li </mi>  <annotation-xml encoding='MathML-Content'>  <ci> PolyLog </ci>  </annotation-xml>  </semantics>  <mn> 2 </mn>  </msub>  <mo> ( </mo>  <msqrt>  <mi> z </mi>  </msqrt>  <mo> ) </mo>  </mrow>  </mrow>  <mrow>  <mn> 512 </mn>  <mo> ⁢ </mo>  <msqrt>  <mi> z </mi>  </msqrt>  </mrow>  </mfrac>  </mrow>  </mrow>  <annotation-xml encoding='MathML-Content'>  <apply>  <eq />  <apply>  <ci> HypergeometricPFQ </ci>  <list>  <apply>  <times />  <cn type='integer'> -1 </cn>  <cn type='rational'> 5 <sep /> 2 </cn>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  <cn type='integer'> 3 </cn>  </list>  <list>  <cn type='rational'> 3 <sep /> 2 </cn>  <cn type='rational'> 3 <sep /> 2 </cn>  </list>  <ci> z </ci>  </apply>  <apply>  <plus />  <apply>  <times />  <apply>  <plus />  <apply>  <times />  <cn type='integer'> -105 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 2 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 490 </cn>  <ci> z </ci>  </apply>  <cn type='integer'> 799 </cn>  </apply>  <apply>  <power />  <cn type='integer'> 1024 </cn>  <cn type='integer'> -1 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <cn type='integer'> 15 </cn>  <apply>  <plus />  <apply>  <times />  <cn type='integer'> 7 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 3 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <cn type='integer'> 35 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 2 </cn>  </apply>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 17 </cn>  <ci> z </ci>  </apply>  <cn type='integer'> 11 </cn>  </apply>  <apply>  <ln />  <apply>  <plus />  <cn type='integer'> 1 </cn>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  </apply>  </apply>  </apply>  <apply>  <power />  <apply>  <times />  <cn type='integer'> 2048 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 15 </cn>  <apply>  <plus />  <apply>  <times />  <cn type='integer'> 7 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 3 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <cn type='integer'> 35 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 2 </cn>  </apply>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 17 </cn>  <ci> z </ci>  </apply>  <cn type='integer'> 11 </cn>  </apply>  <apply>  <ln />  <apply>  <plus />  <apply>  <power />  <ci> z </ci>  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  <cn type='integer'> 1 </cn>  </apply>  </apply>  <apply>  <power />  <apply>  <times />  <cn type='integer'> 2048 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <cn type='integer'> 15 </cn>  <apply>  <plus />  <apply>  <times />  <cn type='integer'> 15 </cn>  <ci> z </ci>  </apply>  <cn type='integer'> 1 </cn>  </apply>  <apply>  <ci> PolyLog </ci>  <cn type='integer'> 2 </cn>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  </apply>  </apply>  <apply>  <power />  <apply>  <times />  <cn type='integer'> 512 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 15 </cn>  <apply>  <plus />  <apply>  <times />  <cn type='integer'> 15 </cn>  <ci> z </ci>  </apply>  <cn type='integer'> 1 </cn>  </apply>  <apply>  <ci> PolyLog </ci>  <cn type='integer'> 2 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  </apply>  <apply>  <power />  <apply>  <times />  <cn type='integer'> 512 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  </apply>  </apply>  </annotation-xml>  </semantics>  </math> 
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 | | Date Added to functions.wolfram.com (modification date) | 
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 | | HypergeometricPFQ[{},{},z] |  | HypergeometricPFQ[{},{b},z] |  | HypergeometricPFQ[{a},{},z] |  | HypergeometricPFQ[{a},{b},z] |  | HypergeometricPFQ[{a1},{b1,b2},z] |  | HypergeometricPFQ[{a1,a2},{b1},z] |  | HypergeometricPFQ[{a1,a2},{b1,b2},z] |  | HypergeometricPFQ[{a1,a2},{b1,b2,b3},z] |  | HypergeometricPFQ[{a1,a2,a3,a4},{b1,b2,b3},z] |  | HypergeometricPFQ[{a1,a2,a3,a4,a5},{b1,b2,b3,b4},z] |  | HypergeometricPFQ[{a1,a2,a3,a4,a5,a6},{b1,b2,b3,b4,b5},z] |  | HypergeometricPFQ[{a1,...,ap},{b1,...,bq},z] |  |  | 
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