Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.6902)

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=2

For fixed z and a₁=-7/2, a₂=1, a₃=2, b₁=-5/2

http://functions.wolfram.com/07.27.03.6902.01

Input Form

HypergeometricPFQ[{-(7/2), 1, 2}, {-(5/2), 5/2}, -z] == -((3 (-17920 - 2880 z + 4704 z^2 - 9800 z^3 + 44100 z^4 + 11025 Pi^2 z^(9/2)))/(51200 z)) + (1/(1638400 (1 + z)^(17/2))) ((2696000 + 21752544 z + 86063464 z^2 + 295105780 z^3 - 176419780 z^4 - 343096685 z^5 - 1097493166 z^6 - 1909844146 z^7 - 2143587600 z^8 - 1572560325 z^9 - 731458350 z^10 - 196441560 z^11 - 23262960 z^12) Log[1 + Sqrt[z] - Sqrt[1 + z]]) + (1/(1638400 (1 + z)^(17/2))) ((-2696000 - 21752544 z - 86063464 z^2 - 295105780 z^3 + 176419780 z^4 + 343096685 z^5 + 1097493166 z^6 + 1909844146 z^7 + 2143587600 z^8 + 1572560325 z^9 + 731458350 z^10 + 196441560 z^11 + 23262960 z^12) Log[1 - Sqrt[z] + Sqrt[1 + z]]) - (21 Sqrt[1 + z] (128 - 144 z + 168 z^2 - 210 z^3 + 315 z^4) Log[Sqrt[z] + Sqrt[1 + z]])/(2560 z^(3/2)) + (1/(1638400 (1 + z)^(17/2))) ((-2696000 - 21752544 z - 86063464 z^2 - 295105780 z^3 + 176419780 z^4 + 343096685 z^5 + 1097493166 z^6 + 1909844146 z^7 + 2143587600 z^8 + 1572560325 z^9 + 731458350 z^10 + 196441560 z^11 + 23262960 z^12) Log[(-1 + Sqrt[z] + Sqrt[1 + z])/ (1 + Sqrt[z] + Sqrt[1 + z])]) - (1323/512) z^(7/2) Log[Sqrt[z] + Sqrt[1 + z]] Log[(-1 + Sqrt[z] + Sqrt[1 + z])/ (1 + Sqrt[z] + Sqrt[1 + z])] - (1323/512) z^(7/2) PolyLog[2, -(1/(Sqrt[z] + Sqrt[1 + z]))] + (1323/512) z^(7/2) PolyLog[2, 1/(Sqrt[z] + Sqrt[1 + z])]

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]