Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a90h)

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=-19/4

http://functions.wolfram.com/07.23.03.a90h.01

Input Form

Hypergeometric2F1[-(19/4), -(19/4), 4, -z] == (256 Sqrt[2] (Sqrt[1 + z] (-234080 - 6898045 z - 156292290 z^2 + 6543019913 z^3 - 22815353324 z^4 + 20161642725 z^5 - 4773572306 z^6 + 209199407 z^7) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] + (-234080 - 7132125 z - 163190335 z^2 + 6386727623 z^3 - 16272333411 z^4 - 2653710599 z^5 + 15388070419 z^6 - 4564372899 z^7 + 209199407 z^8) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - Sqrt[1 + z] (-234080 - 6898045 z - 156292290 z^2 + 6543019913 z^3 - 22815353324 z^4 + 20161642725 z^5 - 4773572306 z^6 + 209199407 z^7) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - (-234080 - 7073605 z - 161449365 z^2 - 633477877 z^3 + 21482884867 z^4 - 50780109207 z^5 + 31299274537 z^6 - 5122874287 z^7 + 140821065 z^8) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])]))/ (903648774105 Pi z^3 Sqrt[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]