Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a91v)

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=-19/4, b>=a

For fixed z and a=-19/4, b=-17/4

http://functions.wolfram.com/07.23.03.a91v.01

Input Form

Hypergeometric2F1[-(19/4), -(17/4), 4, -z] == -((1/(4512611027925 Pi z^3)) (256 (1 + z)^(1/4) (2 (1478048 + 41246777 z + 868260822 z^2 - 59209079625 z^3 + 228230210580 z^4 - 218883022569 z^5 + 56894832534 z^6 - 2890045671 z^7) EllipticE[1/2 - 1/(2 Sqrt[1 + z])] + (-1478048 (1 + Sqrt[1 + z]) - 46189 z (893 + 869 Sqrt[1 + z]) - 277134 z^2 (3133 + 3025 Sqrt[1 + z]) + 3 z^7 (963348557 + 35409725 Sqrt[1 + z]) - 6 z^6 (9482472089 + 1078175117 Sqrt[1 + z]) - 60 z^4 (3803836843 + 1110511231 Sqrt[1 + z]) + 15 z^3 (3947271975 + 1638560999 Sqrt[1 + z]) + 9 z^5 (24320335841 + 4794431321 Sqrt[1 + z])) 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]