Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b93z)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 8 and fixed z and a<0

For fixed z and a=-41/8, b>=a

For fixed z and a=-41/8, b=13/8

http://functions.wolfram.com/07.23.03.b93z.01

Input Form

Hypergeometric2F1[-(41/8), 13/8, 5, z] == (1/(144792971197875 Pi z^4)) (32768 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (-4 (-32117760 + 230511840 z - 637723635 z^2 + 550643940 z^3 - 5303635490 z^4 + 8125816412 z^5 - 6904586643 z^6 + 3502289912 z^7 - 995799728 z^8 + 122751552 z^9) EllipticE[ 1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 5 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (-4014720 + 28155315 z - 75296910 z^2 - 825965910 z^3 + 1298714600 z^4 - 1120043141 z^5 + 574371102 z^6 - 164748848 z^7 + 20458592 z^8) EllipticK[ 1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 3 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] Sqrt[1 - z] (4014720 - 25897035 z + 61182660 z^2 - 1498975170 z^3 + 2433427660 z^4 - 2141916379 z^5 + 1116897672 z^6 - 325113712 z^7 + 40917184 z^8) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 2 (-32117760 + 230511840 z - 637723635 z^2 + 550643940 z^3 - 5303635490 z^4 + 8125816412 z^5 - 6904586643 z^6 + 3502289912 z^7 - 995799728 z^8 + 122751552 z^9) EllipticK[ 1/2 - 1/(Sqrt[2] 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]