Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b7lq)

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=-43/8, b>=a

For fixed z and a=-43/8, b=-9/8

http://functions.wolfram.com/07.23.03.b7lq.01

Input Form

Hypergeometric2F1[-(43/8), -(9/8), 5, z] == (1/(49723887709794375 Pi z^4)) (32768 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (-16 (13176576 - 210413448 z + 1812963033 z^2 - 13920126066 z^3 - 537967746175 z^4 - 525543123810 z^5 - 3361690245 z^6 + 507841170 z^7 - 62761365 z^8 + 4077450 z^9) EllipticE[ 1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 3 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] Sqrt[1 - z] (-6588288 + 100419921 z - 833984613 z^2 - 499456569150 z^3 - 567371622850 z^4 - 12889227195 z^5 + 1959612015 z^6 - 246152520 z^7 + 16309800 z^8) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 8 (13176576 - 210413448 z + 1812963033 z^2 - 13920126066 z^3 - 537967746175 z^4 - 525543123810 z^5 - 3361690245 z^6 + 507841170 z^7 - 62761365 z^8 + 4077450 z^9) EllipticK[ 1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 5 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (-6588288 + 104125833 z - 889727706 z^2 + 310309651575 z^3 + 471123229160 z^4 + 87745061655 z^5 - 6219951330 z^6 + 917185785 z^7 - 107268300 z^8 + 6523920 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]