Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.9351)

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=-5/4

http://functions.wolfram.com/07.23.03.9351.01

Input Form

Hypergeometric2F1[-(23/4), -(5/4), 4, -z] == (1/(93364366095 Pi z^3)) (256 (1 + z)^(1/4) (2 (-153824 - 2831323 z - 35499695 z^2 + 1079828034 z^3 - 1290775302 z^4 + 14818713 z^5 + 2669901 z^6 + 371280 z^7 + 26520 z^8) EllipticE[1/2 - 1/(2 Sqrt[1 + z])] - (-153824 - 2831323 z - 35499695 z^2 + 1079828034 z^3 - 1290775302 z^4 + 14818713 z^5 + 2669901 z^6 + 371280 z^7 + 26520 z^8) EllipticK[1/2 - 1/(2 Sqrt[1 + z])] + Sqrt[1 + z] (153824 + 2715955 z + 33480755 z^2 - 375217974 z^3 + 219751350 z^4 + 26075127 z^5 + 4816695 z^6 + 702780 z^7 + 53040 z^8) 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]