Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.9350)

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/07.23.03.9350.01

Input Form

Hypergeometric2F1[-(23/4), -(5/4), 4, z] == (1/(93364366095 Pi z^3)) (256 Sqrt[1 + Sqrt[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) EllipticE[(2 Sqrt[z])/(1 + Sqrt[z])] + (-153824 + 153824 Sqrt[z] + 2715955 z - 2715955 z^(3/2) - 33480755 z^2 + 33480755 z^(5/2) - 375217974 z^3 + 375217974 z^(7/2) - 219751350 z^4 + 219751350 z^(9/2) + 26075127 z^5 - 26075127 z^(11/2) - 4816695 z^6 + 4816695 z^(13/2) + 702780 z^7 - 702780 z^(15/2) - 53040 z^8 + 53040 z^(17/2)) 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]