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

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=-17/4, b>=a

For fixed z and a=-17/4, b=-3/2

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

Input Form

Hypergeometric2F1[-(17/4), -(3/2), 5, z] == (64 Sqrt[2] (2 (-113152 + 1697280 z - 13751504 z^2 + 100134216 z^3 + 2139642220 z^4 + 1922202221 z^5 + 129606400 z^6 - 8259328 z^7 + 413952 z^8) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + 2 Sqrt[1 - z] (-113152 + 1697280 z - 13751504 z^2 + 100134216 z^3 + 2139642220 z^4 + 1922202221 z^5 + 129606400 z^6 - 8259328 z^7 + 413952 z^8) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (1 - z)^(3/4) (113152 - 1640704 z + 12948832 z^2 - 93907320 z^3 - 848794480 z^4 - 490073491 z^5 - 2641408 z^6 + 137984 z^7) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (-113152 + 1697280 z - 13751504 z^2 + 100134216 z^3 + 2139642220 z^4 + 1922202221 z^5 + 129606400 z^6 - 8259328 z^7 + 413952 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (1 - z)^(1/4) (-113152 + 1697280 z - 13751504 z^2 + 100134216 z^3 + 2139642220 z^4 + 1922202221 z^5 + 129606400 z^6 - 8259328 z^7 + 413952 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - Sqrt[1 - z] (-113152 + 1697280 z - 13751504 z^2 + 100134216 z^3 + 2139642220 z^4 + 1922202221 z^5 + 129606400 z^6 - 8259328 z^7 + 413952 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])]))/ (42748831125 Pi Sqrt[1 + Sqrt[1 - z]] z^4)

Standard Form

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MathML 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]