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

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=7/4

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

Input Form

Hypergeometric2F1[-(17/4), 7/4, 4, z] == (1/(50470875 Pi z^3)) (256 (2 (-21216 + 94809 z - 69615 z^2 + 518575 z^3 - 806725 z^4 + 626124 z^5 - 249856 z^6 + 40960 z^7) EllipticE[(1/2) (1 - Sqrt[1 - z])] + Sqrt[1 - z] (21216 - 89505 z + 49725 z^2 - 120775 z^3 + 117675 z^4 - 55104 z^5 + 10240 z^6) EllipticK[(1/2) (1 - Sqrt[1 - z])] - (-21216 + 94809 z - 69615 z^2 + 518575 z^3 - 806725 z^4 + 626124 z^5 - 249856 z^6 + 40960 z^7) EllipticK[(1/2) (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]