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

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=1/4

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

Input Form

Hypergeometric2F1[-(15/4), 1/4, 6, z] == (1/(18729201645 Pi z^5)) (16384 (-2 Sqrt[1 - z] (-2048 + 20128 z - 91987 z^2 + 269332 z^3 - 660170 z^4 - 488908 z^5 + 127813 z^6 - 25232 z^7 + 2432 z^8) EllipticE[(1/2) (1 - Sqrt[1 - z])] + (-2048 + 21664 z - 106939 z^2 + 336973 z^3 - 856310 z^4 + 2276162 z^5 + 33649 z^6 - 6479 z^7 + 608 z^8) EllipticK[(1/2) (1 - Sqrt[1 - z])] + Sqrt[1 - z] (-2048 + 20128 z - 91987 z^2 + 269332 z^3 - 660170 z^4 - 488908 z^5 + 127813 z^6 - 25232 z^7 + 2432 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]