Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.aj6r)

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=3/4, b>=a

For fixed z and a=3/4, b=19/4

http://functions.wolfram.com/07.23.03.aj6r.01

Input Form

Hypergeometric2F1[3/4, 19/4, -(3/2), z] == (1/(3696 Pi^(3/2))) (((1/(-1 + z)^7) (2 (-924 + 8547 z - 55825 z^2 - 25095 z^3 + 10305 z^4 - 2928 z^5 + 384 z^6) EllipticE[(1/2) (1 - Sqrt[z])]) + (1/(-1 + z)^7) (2 (-924 + 8547 z - 55825 z^2 - 25095 z^3 + 10305 z^4 - 2928 z^5 + 384 z^6) EllipticE[(1/2) (1 + Sqrt[z])]) + (1/((-1 + Sqrt[z])^7 (1 + Sqrt[z])^6)) ((924 - 462 Sqrt[z] - 8085 z + 3850 z^(3/2) + 51975 z^2 + 19110 z^(5/2) + 5985 z^3 - 8370 z^(7/2) - 1935 z^4 + 2640 z^(9/2) + 288 z^5 - 384 z^(11/2)) EllipticK[(1/2) (1 - Sqrt[z])]) - (1/((-1 + Sqrt[z])^6 (1 + Sqrt[z])^7)) ((924 + 462 Sqrt[z] - 8085 z - 3850 z^(3/2) + 51975 z^2 - 19110 z^(5/2) + 5985 z^3 + 8370 z^(7/2) - 1935 z^4 - 2640 z^(9/2) + 288 z^5 + 384 z^(11/2)) EllipticK[(1/2) (1 + Sqrt[z])])) Gamma[1/4]^2)

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]