Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a97w)

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=-7/4

http://functions.wolfram.com/07.23.03.a97w.01

Input Form

Hypergeometric2F1[-(19/4), -(7/4), 5, z] == (1/(16194422475 Pi z^4)) (4096 (2 Sqrt[1 - z] (-384 + 6224 z - 55811 z^2 + 469371 z^3 + 5332610 z^4 + 4231846 z^5 + 213969 z^6 - 14881 z^7 + 736 z^8) EllipticE[(1/2) (1 - Sqrt[1 - z])] - 4 (-96 + 1628 z - 15113 z^2 + 127701 z^3 - 730780 z^4 - 3112706 z^5 - 1361577 z^6 - 943 z^7 + 46 z^8) EllipticK[(1/2) (1 - Sqrt[1 - z])] - Sqrt[1 - z] (-384 + 6224 z - 55811 z^2 + 469371 z^3 + 5332610 z^4 + 4231846 z^5 + 213969 z^6 - 14881 z^7 + 736 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]