Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.ae0f)

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=-5/2, b>=a

For fixed z and a=-5/2, b=23/4

http://functions.wolfram.com/07.23.03.ae0f.01

Input Form

Hypergeometric2F1[-(5/2), 23/4, 4, z] == (1/(724185 Pi Sqrt[1 + Sqrt[1 - z]] z^3)) (4 Sqrt[2] (2 (-256 - 1968 z - 16592 z^2 + 358020 z^3 - 815490 z^4 + 480675 z^5) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + 2 Sqrt[1 - z] (-256 - 1968 z - 16592 z^2 + 358020 z^3 - 815490 z^4 + 480675 z^5) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (-256 - 1968 z - 16592 z^2 + 358020 z^3 - 815490 z^4 + 480675 z^5) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (1 - z)^(1/4) (-256 - 1968 z - 16592 z^2 + 358020 z^3 - 815490 z^4 + 480675 z^5) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - Sqrt[1 - z] (-256 - 1968 z - 16592 z^2 + 358020 z^3 - 815490 z^4 + 480675 z^5) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (1 - z)^(3/4) (256 + 2096 z + 17680 z^2 + 13260 z^3 - 430950 z^4 + 480675 z^5) EllipticK[1/2 - (1 - z)^(1/4)/(1 + 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]