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

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=2, a₃>=2

For fixed z and a₁=-5/2, a₂=2, a₃=3

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

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

Input Form

HypergeometricPFQ[{-(5/2), 2, 3}, {-(3/2), 5/2}, -z] == (3 (-320 + 1824 z - 5096 z^2 + 34300 z^3 + 11025 Pi^2 z^(7/2) + 44100 z^4 + 11025 Pi^2 z^(9/2)))/(8192 z (1 + z)) + (1/(98304 (1 + z)^(17/2))) ((-340224 - 1832064 z - 11829600 z^2 - 31597120 z^3 - 246860140 z^4 - 672057114 z^5 - 1147216549 z^6 - 1270966105 z^7 - 922348665 z^8 - 425005425 z^9 - 113193990 z^10 - 13304340 z^11) Log[1 + Sqrt[z] - Sqrt[1 + z]]) + (1/(98304 (1 + z)^(17/2))) ((340224 + 1832064 z + 11829600 z^2 + 31597120 z^3 + 246860140 z^4 + 672057114 z^5 + 1147216549 z^6 + 1270966105 z^7 + 922348665 z^8 + 425005425 z^9 + 113193990 z^10 + 13304340 z^11) Log[1 - Sqrt[z] + Sqrt[1 + z]]) + (15 (16 + 56 z - 126 z^2 + 441 z^3 + 2940 z^4 + 2205 z^5) Log[Sqrt[z] + Sqrt[1 + z]])/(2048 z^(3/2) (1 + z)^(3/2)) + (1/(98304 (1 + z)^(17/2))) ((340224 + 1832064 z + 11829600 z^2 + 31597120 z^3 + 246860140 z^4 + 672057114 z^5 + 1147216549 z^6 + 1270966105 z^7 + 922348665 z^8 + 425005425 z^9 + 113193990 z^10 + 13304340 z^11) Log[(-1 + Sqrt[z] + Sqrt[1 + z])/ (1 + Sqrt[z] + Sqrt[1 + z])]) + (33075 z^(5/2) Log[Sqrt[z] + Sqrt[1 + z]] Log[(-1 + Sqrt[z] + Sqrt[1 + z])/(1 + Sqrt[z] + Sqrt[1 + z])])/2048 + (33075 z^(5/2) PolyLog[2, -(1/(Sqrt[z] + Sqrt[1 + z]))])/2048 - (33075 z^(5/2) PolyLog[2, 1/(Sqrt[z] + Sqrt[1 + z])])/2048

Standard Form

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MathML 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]