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

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=-15/4, b>=a

For fixed z and a=-15/4, b=-1/4

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

Input Form

Hypergeometric2F1[-(15/4), -(1/4), 4, z] == (1/(177161985 Pi Sqrt[1 + Sqrt[z]] z^3)) (256 ((2464 + 2464 Sqrt[z] - 26565 z - 26565 z^(3/2) + 170016 z^2 + 170016 z^(5/2) + 1657074 z^3 + 1657074 z^(7/2) + 38844 z^4 + 38844 z^(9/2) - 7605 z^5 - 7605 z^(11/2) + 780 z^6 + 780 z^(13/2)) EllipticE[(2 Sqrt[z])/(1 + Sqrt[z])] - (2464 - 27181 z + 176484 z^2 + 232266 z^3 - 451308 z^4 + 81315 z^5 - 15600 z^6 + 1560 z^7) EllipticK[(2 Sqrt[z])/(1 + Sqrt[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,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]