Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.aa8c)

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=-17/4, b>=a

For fixed z and a=-17/4, b=-15/4

http://functions.wolfram.com/07.23.03.aa8c.01

Input Form

Hypergeometric2F1[-(17/4), -(15/4), 2, -z] == (1/(14549535 Pi z)) (8 (1 + z)^(1/4) (2 (-36465 + 6665519 z - 39238362 z^2 + 44228590 z^3 - 10252965 z^4 + 241395 z^5) EllipticE[1/2 - 1/(2 Sqrt[1 + z])] + (-241395 z^5 + 36465 (1 + Sqrt[1 + z]) + 15 z^4 (683531 + 65215 Sqrt[1 + z]) - 10 z^3 (4422859 + 877414 Sqrt[1 + z]) + 6 z^2 (6539727 + 2053585 Sqrt[1 + z]) - z (6665519 + 3055484 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]