Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.9075)

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=-17/4

http://functions.wolfram.com/07.23.03.9075.01

Input Form

Hypergeometric2F1[-(23/4), -(17/4), 1, -z] == -((1/(334639305 Pi)) (2 (1 + z)^(1/4) (2 (-728420683 + 12959599657 z - 38890777198 z^2 + 27874724562 z^3 - 4101448695 z^4 + 2197845 z^5) EllipticE[1/2 - 1/(2 Sqrt[1 + z])] + (728420683 + 393781378 Sqrt[1 + z] + 2197845 z^5 (-1 + 2 Sqrt[1 + z]) + 15 z^4 (273429913 + 19047990 Sqrt[1 + z]) - 6 z^3 (4645787427 + 792850090 Sqrt[1 + z]) - z (12959599657 + 5056272718 Sqrt[1 + z]) + 2 z^2 (19445388599 + 5325406682 Sqrt[1 + z])) EllipticK[1/2 - 1/(2 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,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]