Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.9794)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 4 and fixed z

For fixed z and a=-23/4, b>=a

For fixed z and a=-23/4, b=11/4

http://functions.wolfram.com/07.23.03.9794.01

Input Form

Hypergeometric2F1[-(23/4), 11/4, 5, z] == (4096 (-8 (76912 + 76912 Sqrt[z] - 298034 z - 298034 z^(3/2) + 120175 z^2 + 120175 z^(5/2) + 336490 z^3 + 336490 z^(7/2) - 2618070 z^4 - 2618070 z^(9/2) + 5492214 z^5 + 5492214 z^(11/2) - 5951673 z^6 - 5951673 z^(13/2) + 3659370 z^7 + 3659370 z^(15/2) - 1218360 z^8 - 1218360 z^(17/2) + 171600 z^9 + 171600 z^(19/2)) EllipticE[(2 Sqrt[z])/(1 + Sqrt[z])] + (615296 - 2538096 z + 1514205 z^2 + 2595780 z^3 + 9676030 z^4 - 55811028 z^5 + 106093533 z^6 - 107825640 z^7 + 63114480 z^8 - 20180160 z^9 + 2745600 z^10) EllipticK[(2 Sqrt[z])/(1 + Sqrt[z])]))/ (64073584575 Pi Sqrt[1 + Sqrt[z]] z^4)

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,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},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]