Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.ad2r)

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=-5/2, a₂>=-5/2

For fixed z and a₁=-5/2, a₂=3, a₃>=3

For fixed z and a₁=-5/2, a₂=3, a₃=3

For fixed z and a₁=-5/2, a₂=3, a₃=3, b₁=1/2

http://functions.wolfram.com/07.27.03.ad2r.01

Input Form

HypergeometricPFQ[{-(5/2), 3, 3}, {1/2, 5/2}, -z] == (1/(262144 z)) (-960 + 245024 z + 162000 Pi^2 z^(3/2) + 2734200 z^2 + 882000 Pi^2 z^(5/2) + 3572100 z^3 + 893025 Pi^2 z^(7/2)) + (1/(393216 (1 + z)^(15/2))) ((-877056 - 19952160 z - 165841440 z^2 - 668224090 z^3 - 1636438140 z^4 - 2607365596 z^5 - 2780493520 z^6 - 1977882195 z^7 - 903637675 z^8 - 240443175 z^9 - 28381185 z^10) Log[1 + Sqrt[z] - Sqrt[1 + z]]) + (1/(393216 (1 + z)^(15/2))) ((877056 + 19952160 z + 165841440 z^2 + 668224090 z^3 + 1636438140 z^4 + 2607365596 z^5 + 2780493520 z^6 + 1977882195 z^7 + 903637675 z^8 + 240443175 z^9 + 28381185 z^10) Log[1 - Sqrt[z] + Sqrt[1 + z]]) + (15 (16 + 296 z + 22462 z^2 + 78645 z^3 + 59535 z^4) Log[Sqrt[z] + Sqrt[1 + z]])/(65536 z^(3/2) Sqrt[1 + z]) + (1/(393216 (1 + z)^(15/2))) ((877056 + 19952160 z + 165841440 z^2 + 668224090 z^3 + 1636438140 z^4 + 2607365596 z^5 + 2780493520 z^6 + 1977882195 z^7 + 903637675 z^8 + 240443175 z^9 + 28381185 z^10) Log[(-1 + Sqrt[z] + Sqrt[1 + z])/(1 + Sqrt[z] + Sqrt[1 + z])]) + (225 Sqrt[z] (720 + 3920 z + 3969 z^2) Log[Sqrt[z] + Sqrt[1 + z]] Log[(-1 + Sqrt[z] + Sqrt[1 + z])/(1 + Sqrt[z] + Sqrt[1 + z])])/65536 + (225 Sqrt[z] (720 + 3920 z + 3969 z^2) PolyLog[2, -(1/(Sqrt[z] + Sqrt[1 + z]))])/65536 - (225 Sqrt[z] (720 + 3920 z + 3969 z^2) PolyLog[2, 1/(Sqrt[z] + Sqrt[1 + z])])/65536

Standard Form

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MathML Form

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2780493520 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2607365596 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 1636438140 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 668224090 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 165841440 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 19952160 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 877056 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mfrac> <mrow> <msqrt> <mi> z </mi> </msqrt> <mo> + </mo> <msqrt> <mrow> <mi> z </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msqrt> <mo> - </mo> <mn> 1 </mn> </mrow> <mrow> <msqrt> <mi> z </mi> </msqrt> <mo> + </mo> <msqrt> <mrow> <mi> z </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msqrt> <mo> + </mo> <mn> 1 </mn> 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Rule Form

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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]