Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a869)

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=-21/4, b>=a

For fixed z and a=-21/4, b=-19/4

http://functions.wolfram.com/07.23.03.a869.01

Input Form

Hypergeometric2F1[-(21/4), -(19/4), 3, -z] == (1/(145568097675 Pi z^2)) (64 (1 + z)^(1/4) (-2 (1293292 + 63047985 z - 8226663318 z^2 + 52727147895 z^3 - 84034916280 z^4 + 39224536239 z^5 - 4640248830 z^6 + 63293769 z^7) EllipticE[1/2 - 1/(2 Sqrt[1 + z])] - 4 Sqrt[1 + z] (-323323 - 15519504 z + 931016805 z^2 - 4357378920 z^3 + 4941663615 z^4 - 1480865736 z^5 + 85038807 z^6) EllipticK[1/2 - 1/(2 Sqrt[1 + z])] + (1293292 + 63047985 z - 8226663318 z^2 + 52727147895 z^3 - 84034916280 z^4 + 39224536239 z^5 - 4640248830 z^6 + 63293769 z^7) 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]