Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.abh0)

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=7/4

http://functions.wolfram.com/07.23.03.abh0.01

Input Form

Hypergeometric2F1[-(15/4), 7/4, 6, -z] == (1/(5492021535 Pi z^5)) (16384 (1 + z)^(1/4) (2 (22528 + 155936 z + 437745 z^2 + 582120 z^3 + 150150 z^4 + 263484 z^5 + 184353 z^6 + 64740 z^7 + 9360 z^8) EllipticE[1/2 - 1/(2 Sqrt[1 + z])] - (22528 + 155936 z + 437745 z^2 + 582120 z^3 + 150150 z^4 + 263484 z^5 + 184353 z^6 + 64740 z^7 + 9360 z^8) EllipticK[1/2 - 1/(2 Sqrt[1 + z])] + Sqrt[1 + z] (-22528 - 139040 z - 336105 z^2 - 345345 z^3 + 75075 z^4 + 322101 z^5 + 283530 z^6 + 115440 z^7 + 18720 z^8) 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]