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

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=-3/4

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

Input Form

Hypergeometric2F1[-(17/4), -(3/4), 6, -z] == (1/(138241170092025 Pi z^5)) (16384 (1 + z)^(1/4) (-2 (1357824 + 17800224 z + 114674469 z^2 + 513972849 z^3 + 2206643010 z^4 - 20791185382 z^5 + 6104500633 z^6 + 559818413 z^7 + 62990928 z^8 + 4037880 z^9) EllipticE[1/2 - 1/(2 Sqrt[1 + z])] + Sqrt[1 + z] (1357824 + 16781856 z + 102247197 z^2 + 439194405 z^3 + 1888522350 z^4 - 5285100502 z^5 + 252804937 z^6 + 29644769 z^7 + 2018940 z^8) EllipticK[1/2 - 1/(2 Sqrt[1 + z])] + (1357824 + 17800224 z + 114674469 z^2 + 513972849 z^3 + 2206643010 z^4 - 20791185382 z^5 + 6104500633 z^6 + 559818413 z^7 + 62990928 z^8 + 4037880 z^9) 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]