Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.abe9)

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=1, a₃>=1

For fixed z and a₁=-5/2, a₂=1, a₃=3

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

http://functions.wolfram.com/07.27.03.abe9.01

Input Form

HypergeometricPFQ[{-(5/2), 1, 3}, {-(3/2), 1/2}, -z] == (1/(256 (1 + z)^2)) (256 - 1448 z + 12516 z^2 + 4725 Pi^2 z^(5/2) + 33600 z^3 + 9450 Pi^2 z^(7/2) + 18900 z^4 + 4725 Pi^2 z^(9/2)) + (1/(6144 (1 + z)^(15/2))) ((-6144 + 45600 z - 294160 z^2 - 6448460 z^3 - 29478630 z^4 - 70449259 z^5 - 100388690 z^6 - 89149725 z^7 - 48626100 z^8 - 14969700 z^9 - 1997640 z^10) Log[1 + Sqrt[z] - Sqrt[1 + z]]) + (1/(6144 (1 + z)^(15/2))) ((6144 - 45600 z + 294160 z^2 + 6448460 z^3 + 29478630 z^4 + 70449259 z^5 + 100388690 z^6 + 89149725 z^7 + 48626100 z^8 + 14969700 z^9 + 1997640 z^10) Log[1 - Sqrt[z] + Sqrt[1 + z]]) + (15 (-10 Sqrt[z] + 45 z^(3/2) + 483 z^(5/2) + 735 z^(7/2) + 315 z^(9/2)) Log[Sqrt[z] + Sqrt[1 + z]])/(64 (1 + z)^(5/2)) + (1/(6144 (1 + z)^(15/2))) ((6144 - 45600 z + 294160 z^2 + 6448460 z^3 + 29478630 z^4 + 70449259 z^5 + 100388690 z^6 + 89149725 z^7 + 48626100 z^8 + 14969700 z^9 + 1997640 z^10) Log[(-1 + Sqrt[z] + Sqrt[1 + z])/(1 + Sqrt[z] + Sqrt[1 + z])]) + (4725/64) z^(5/2) Log[Sqrt[z] + Sqrt[1 + z]] Log[(-1 + Sqrt[z] + Sqrt[1 + z])/(1 + Sqrt[z] + Sqrt[1 + z])] + (4725/64) z^(5/2) PolyLog[2, -(1/(Sqrt[z] + Sqrt[1 + z]))] - (4725/64) z^(5/2) PolyLog[2, 1/(Sqrt[z] + Sqrt[1 + z])]

Standard Form

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MathML Form

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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]