Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.9034)

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=-23/4, b>=a

For fixed z and a=-23/4, b=-19/4

http://functions.wolfram.com/07.23.03.9034.01

Input Form

Hypergeometric2F1[-(23/4), -(19/4), 3, z] == (1/(3802168755 Pi z^2)) (64 (2 Sqrt[1 - z] (-29260 + 1514205 z + 124570242 z^2 + 720942791 z^3 + 1049030640 z^4 + 437491899 z^5 + 42473978 z^6 + 197505 z^7) EllipticE[(1/2) (1 - Sqrt[1 - z])] - Sqrt[1 - z] (-29260 + 1514205 z + 124570242 z^2 + 720942791 z^3 + 1049030640 z^4 + 437491899 z^5 + 42473978 z^6 + 197505 z^7) EllipticK[(1/2) (1 - Sqrt[1 - z])] + 2 (14630 - 768075 z - 2309436 z^2 + 223450559 z^3 + 919496454 z^4 + 942940179 z^5 + 275789744 z^6 + 17577945 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]