Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.9091)

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=-23/4, b>=a

For fixed z and a=-23/4, b=-17/4

http://functions.wolfram.com/07.23.03.9091.01

Input Form

Hypergeometric2F1[-(23/4), -(17/4), 5, -z] == (1/(473824157932125 Pi z^4)) (4096 (1 + z)^(1/4) (-2 (950912 + 25318032 z + 399672771 z^2 + 6455392405 z^3 - 384292630785 z^4 + 1453856058249 z^5 - 1499540097111 z^6 + 469529178687 z^7 - 34984474155 z^8 + 8171475 z^9) EllipticE[1/2 - 1/(2 Sqrt[1 + z])] + (950912 + 25318032 z + 399672771 z^2 + 6455392405 z^3 - 384292630785 z^4 + 1453856058249 z^5 - 1499540097111 z^6 + 469529178687 z^7 - 34984474155 z^8 + 8171475 z^9) EllipticK[1/2 - 1/(2 Sqrt[1 + z])] - 2 Sqrt[1 + z] (-475456 - 12302424 z - 190665285 z^2 - 3086118035 z^3 + 78759364215 z^4 - 213736454127 z^5 + 154606745937 z^6 - 30127630905 z^7 + 907033725 z^8 + 8171475 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]