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

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=-15/4, b>=a

For fixed z and a=-15/4, b=13/4

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

Input Form

Hypergeometric2F1[-(15/4), 13/4, 6, z] == (1/(2957242365 Pi z^5)) (16384 (-2 Sqrt[1 - z] (22528 - 73568 z + 44737 z^2 + 41503 z^3 + 67375 z^4 - 452879 z^5 + 590464 z^6 - 321536 z^7 + 65536 z^8) EllipticE[(1/2) (1 - Sqrt[1 - z])] + (22528 - 90464 z + 98329 z^2 + 12397 z^3 + 35035 z^4 - 145649 z^5 + 168112 z^6 - 84992 z^7 + 16384 z^8) EllipticK[(1/2) (1 - Sqrt[1 - z])] + Sqrt[1 - z] (22528 - 73568 z + 44737 z^2 + 41503 z^3 + 67375 z^4 - 452879 z^5 + 590464 z^6 - 321536 z^7 + 65536 z^8) 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]