Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.6715)

HypergeometricPFQ

$Mathematica Notation$

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=-7/2, a₂>=-7/2

For fixed z and a₁=-7/2, a₂=1, a₃>=1

For fixed z and a₁=-7/2, a₂=1, a₃=1

For fixed z and a₁=-7/2, a₂=1, a₃=1, b₁=3/2

http://functions.wolfram.com/07.27.03.6715.01

Input Form

HypergeometricPFQ[{-(7/2), 1, 1}, {3/2, 3/2}, -z] == (1/(589824 Sqrt[z])) (40320 Pi^2 + 260544 Sqrt[z] + 80640 Pi^2 z + 322784 z^(3/2) + 90720 Pi^2 z^2 + 191800 z^(5/2) + 50400 Pi^2 z^3 + 44100 z^(7/2) + 11025 Pi^2 z^4) + (1/(36864 (1 + z)^(5/2))) ((-26784 - 132914 z - 270629 z^2 - 295134 z^3 - 184620 z^4 - 63315 z^5 - 9240 z^6) Log[1 + Sqrt[z] - Sqrt[1 + z]]) + (1/(36864 (1 + z)^(5/2))) ((26784 + 132914 z + 270629 z^2 + 295134 z^3 + 184620 z^4 + 63315 z^5 + 9240 z^6) Log[1 - Sqrt[z] + Sqrt[1 + z]]) + (175 Sqrt[1 + z] (80 + 120 z + 82 z^2 + 21 z^3) Log[Sqrt[z] + Sqrt[1 + z]])/ (49152 Sqrt[z]) + (1/(36864 (1 + z)^(5/2))) ((26784 + 132914 z + 270629 z^2 + 295134 z^3 + 184620 z^4 + 63315 z^5 + 9240 z^6) Log[(-1 + Sqrt[z] + Sqrt[1 + z])/(1 + Sqrt[z] + Sqrt[1 + z])]) + (35 (128 + 256 z + 288 z^2 + 160 z^3 + 35 z^4) Log[Sqrt[z] + Sqrt[1 + z]] Log[(-1 + Sqrt[z] + Sqrt[1 + z])/ (1 + Sqrt[z] + Sqrt[1 + z])])/(16384 Sqrt[z]) + (35 (128 + 256 z + 288 z^2 + 160 z^3 + 35 z^4) PolyLog[2, -(1/(Sqrt[z] + Sqrt[1 + z]))])/(16384 Sqrt[z]) - (35 (128 + 256 z + 288 z^2 + 160 z^3 + 35 z^4) PolyLog[2, 1/(Sqrt[z] + Sqrt[1 + z])])/(16384 Sqrt[z])

Standard Form

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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>   </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> 7 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> , </mo> <mn> 1 </mn> <mo> , </mo> <mn> 1 </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> <mrow> <mo> - </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "3"], SubscriptBox["F", "2"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List["-", FractionBox["7", "2"]]], HypergeometricPFQ, Rule[Editable, True], 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RowBox[List["256", " ", "z"]], "+", RowBox[List["288", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["160", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["35", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", RowBox[List["PolyLog", "[", RowBox[List["2", ",", FractionBox["1", RowBox[List[SqrtBox["z"], "+", SqrtBox[RowBox[List["1", "+", "z"]]]]]]]], "]"]]]], RowBox[List["16384", " ", SqrtBox["z"]]]]]]]]]]

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

2007-05-02

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,...,a_p},{b₁,...,b_q},z]