Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b7pi)

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=1/8

http://functions.wolfram.com/07.23.03.b7pi.01

Input Form

Hypergeometric2F1[-(43/8), 1/8, 5, z] == (65536 2^(1/4) (-4 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (41412096 - 487886256 z + 2862853785 z^2 - 13022971830 z^3 - 51396840290 z^4 + 17063664304 z^5 - 6895410879 z^6 + 2132804030 z^7 - 418445440 z^8 + 38330880 z^9) EllipticE[ 1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + (82824192 - 1006831584 z + 6083129547 z^2 - 28097540955 z^3 + 216893950430 z^4 + 9094247978 z^5 - 3630094761 z^6 + 1103924353 z^7 - 212816240 z^8 + 19165440 z^9) EllipticK[ 1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 2 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (41412096 - 487886256 z + 2862853785 z^2 - 13022971830 z^3 - 51396840290 z^4 + 17063664304 z^5 - 6895410879 z^6 + 2132804030 z^7 - 418445440 z^8 + 38330880 z^9) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 2 Sqrt[1 - z] (41412096 - 487886256 z + 2862853785 z^2 - 13022971830 z^3 - 51396840290 z^4 + 17063664304 z^5 - 6895410879 z^6 + 2132804030 z^7 - 418445440 z^8 + 38330880 z^9) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))/ (10173065118244875 Pi (1 + Sqrt[1 - z])^(1/4) z^4)

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]