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   http://functions.wolfram.com/07.23.03.0068.01
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    Hypergeometric2F1[3/2, b, (2 b + 5)/4, (1 - Sqrt[2])/2] == 
 2^(2 - b/2) Sqrt[Pi] (Gamma[(2 b + 5)/4]/(Gamma[(b + 1)/4] 
     Gamma[(b + 2)/4]) - Gamma[(2 b + 5)/4]/(Gamma[b/4] Gamma[(b + 3)/4])) 
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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> 2 </mn>  </msub>  <msub>  <mi> F </mi>  <mn> 1 </mn>  </msub>  </mrow>  <mo> ⁡ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mfrac>  <mn> 3 </mn>  <mn> 2 </mn>  </mfrac>  <mo> , </mo>  <mi> b </mi>  </mrow>  <mo> ; </mo>  <mfrac>  <mrow>  <mrow>  <mn> 2 </mn>  <mo> ⁢ </mo>  <mi> b </mi>  </mrow>  <mo> + </mo>  <mn> 5 </mn>  </mrow>  <mn> 4 </mn>  </mfrac>  <mo> ; </mo>  <mfrac>  <mrow>  <mn> 1 </mn>  <mo> - </mo>  <msqrt>  <mn> 2 </mn>  </msqrt>  </mrow>  <mn> 2 </mn>  </mfrac>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["2", TraditionalForm]], SubscriptBox["F", FormBox["1", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox["3", "2"], Hypergeometric2F1, Rule[Editable, True]], ",", TagBox["b", Hypergeometric2F1, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1, Rule[Editable, False]], ";", TagBox[TagBox[TagBox[FractionBox[RowBox[List[RowBox[List["2", "b"]], "+", "5"]], "4"], Hypergeometric2F1, Rule[Editable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1, Rule[Editable, False]], ";", TagBox[FractionBox[RowBox[List["1", "-", SqrtBox["2"]]], "2"], Hypergeometric2F1, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], Hypergeometric2F1] </annotation>  </semantics>  <mo> ⩵ </mo>  <mrow>  <msup>  <mn> 2 </mn>  <mrow>  <mn> 2 </mn>  <mo> - </mo>  <mfrac>  <mi> b </mi>  <mn> 2 </mn>  </mfrac>  </mrow>  </msup>  <mo> ⁢ </mo>  <msqrt>  <mi> π </mi>  </msqrt>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mfrac>  <mrow>  <mi> Γ </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <mfrac>  <mrow>  <mrow>  <mn> 2 </mn>  <mo> ⁢ </mo>  <mi> b </mi>  </mrow>  <mo> + </mo>  <mn> 5 </mn>  </mrow>  <mn> 4 </mn>  </mfrac>  <mo> ) </mo>  </mrow>  <mrow>  <mrow>  <mi> Γ </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <mfrac>  <mrow>  <mi> b </mi>  <mo> + </mo>  <mn> 1 </mn>  </mrow>  <mn> 4 </mn>  </mfrac>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <mrow>  <mi> Γ </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <mfrac>  <mrow>  <mi> b </mi>  <mo> + </mo>  <mn> 2 </mn>  </mrow>  <mn> 4 </mn>  </mfrac>  <mo> ) </mo>  </mrow>  </mrow>  </mfrac>  <mo> - </mo>  <mfrac>  <mrow>  <mi> Γ </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <mfrac>  <mrow>  <mrow>  <mn> 2 </mn>  <mo> ⁢ </mo>  <mi> b </mi>  </mrow>  <mo> + </mo>  <mn> 5 </mn>  </mrow>  <mn> 4 </mn>  </mfrac>  <mo> ) </mo>  </mrow>  <mrow>  <mrow>  <mi> Γ </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <mfrac>  <mi> b </mi>  <mn> 4 </mn>  </mfrac>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <mrow>  <mi> Γ </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <mfrac>  <mrow>  <mi> b </mi>  <mo> + </mo>  <mn> 3 </mn>  </mrow>  <mn> 4 </mn>  </mfrac>  <mo> ) </mo>  </mrow>  </mrow>  </mfrac>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  </mrow>  <annotation-xml encoding='MathML-Content'>  <apply>  <eq />  <apply>  <ci> Hypergeometric2F1 </ci>  <cn type='rational'> 3 <sep /> 2 </cn>  <ci> b </ci>  <apply>  <times />  <apply>  <plus />  <apply>  <times />  <cn type='integer'> 2 </cn>  <ci> b </ci>  </apply>  <cn type='integer'> 5 </cn>  </apply>  <apply>  <power />  <cn type='integer'> 4 </cn>  <cn type='integer'> -1 </cn>  </apply>  </apply>  <apply>  <times />  <apply>  <plus />  <cn type='integer'> 1 </cn>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <power />  <cn type='integer'> 2 </cn>  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  </apply>  </apply>  <apply>  <power />  <cn type='integer'> 2 </cn>  <cn type='integer'> -1 </cn>  </apply>  </apply>  </apply>  <apply>  <times />  <apply>  <power />  <cn type='integer'> 2 </cn>  <apply>  <plus />  <cn type='integer'> 2 </cn>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <ci> b </ci>  <apply>  <power />  <cn type='integer'> 2 </cn>  <cn type='integer'> -1 </cn>  </apply>  </apply>  </apply>  </apply>  </apply>  <apply>  <power />  <pi />  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  <apply>  <plus />  <apply>  <times />  <apply>  <ci> Gamma </ci>  <apply>  <times />  <apply>  <plus />  <apply>  <times />  <cn type='integer'> 2 </cn>  <ci> b </ci>  </apply>  <cn type='integer'> 5 </cn>  </apply>  <apply>  <power />  <cn type='integer'> 4 </cn>  <cn type='integer'> -1 </cn>  </apply>  </apply>  </apply>  <apply>  <power />  <apply>  <times />  <apply>  <ci> Gamma </ci>  <apply>  <times />  <apply>  <plus />  <ci> b </ci>  <cn type='integer'> 1 </cn>  </apply>  <apply>  <power />  <cn type='integer'> 4 </cn>  <cn type='integer'> -1 </cn>  </apply>  </apply>  </apply>  <apply>  <ci> Gamma </ci>  <apply>  <times />  <apply>  <plus />  <ci> b </ci>  <cn type='integer'> 2 </cn>  </apply>  <apply>  <power />  <cn type='integer'> 4 </cn>  <cn type='integer'> -1 </cn>  </apply>  </apply>  </apply>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <apply>  <ci> Gamma </ci>  <apply>  <times />  <apply>  <plus />  <apply>  <times />  <cn type='integer'> 2 </cn>  <ci> b </ci>  </apply>  <cn type='integer'> 5 </cn>  </apply>  <apply>  <power />  <cn type='integer'> 4 </cn>  <cn type='integer'> -1 </cn>  </apply>  </apply>  </apply>  <apply>  <power />  <apply>  <times />  <apply>  <ci> Gamma </ci>  <apply>  <times />  <ci> b </ci>  <apply>  <power />  <cn type='integer'> 4 </cn>  <cn type='integer'> -1 </cn>  </apply>  </apply>  </apply>  <apply>  <ci> Gamma </ci>  <apply>  <times />  <apply>  <plus />  <ci> b </ci>  <cn type='integer'> 3 </cn>  </apply>  <apply>  <power />  <cn type='integer'> 4 </cn>  <cn type='integer'> -1 </cn>  </apply>  </apply>  </apply>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  </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,b2},z] |  | HypergeometricPFQ[{a1,a2},{b1,b2,b3},z] |  | HypergeometricPFQ[{a1,a2,a3},{b1,b2},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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