Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.ab3t)

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=-11/4

http://functions.wolfram.com/07.23.03.ab3t.01

Input Form

Hypergeometric2F1[-(15/4), -(11/4), 6, z] == (1/(17169326707995 Pi z^5)) (16384 (2 Sqrt[1 - z] (22528 - 369248 z + 3124737 z^2 - 19823342 z^3 + 136264975 z^4 + 1395008028 z^5 + 1254029167 z^6 + 197247442 z^7 + 1341153 z^8) EllipticE[(1/2) (1 - Sqrt[1 - z])] - Sqrt[1 - z] (22528 - 369248 z + 3124737 z^2 - 19823342 z^3 + 136264975 z^4 + 1395008028 z^5 + 1254029167 z^6 + 197247442 z^7 + 1341153 z^8) EllipticK[(1/2) (1 - Sqrt[1 - z])] + (-22528 + 386144 z - 3400089 z^2 + 22141658 z^3 - 150924235 z^4 + 801755772 z^5 + 3272501729 z^6 + 1815561386 z^7 + 175691043 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]