Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.afhw)

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=-7/4, b>=a

For fixed z and a=-7/4, b=23/4

http://functions.wolfram.com/07.23.03.afhw.01

Input Form

Hypergeometric2F1[-(7/4), 23/4, 6, z] == (16384 ((-(2048 + 2048 Sqrt[z] + 2976 z + 2976 z^(3/2) + 5043 z^2 + 5043 z^(5/2) + 10689 z^3 + 10689 z^(7/2) + 35784 z^4 + 35784 z^(9/2) - 198000 z^5 - 198000 z^(11/2) + 137280 z^6 + 137280 z^(13/2))) EllipticE[(2 Sqrt[z])/(1 + Sqrt[z])] + (2048 + 2464 z + 4155 z^2 + 9141 z^3 + 32592 z^4 + 139680 z^5 - 464640 z^6 + 274560 z^7) EllipticK[(2 Sqrt[z])/(1 + Sqrt[z])]))/ (2848219605 Pi Sqrt[1 + Sqrt[z]] z^5)

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]