Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b4vw)

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=-47/8, b>=a

For fixed z and a=-47/8, b=-13/8

http://functions.wolfram.com/07.23.03.b4vw.01

Input Form

Hypergeometric2F1[-(47/8), -(13/8), 5, z] == (65536 2^(1/4) (-8 Sqrt[1 - z] (111524608 - 2003957800 z + 20107102665 z^2 - 190868267590 z^3 - 2639773676435 z^4 - 2491726929090 z^5 - 106053479805 z^6 + 13152093630 z^7 - 1406686905 z^8 + 81601650 z^9) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - 4 Sqrt[2 - 2 Sqrt[1 - z]] Sqrt[1 - z] (111524608 - 2003957800 z + 20107102665 z^2 - 190868267590 z^3 - 2639773676435 z^4 - 2491726929090 z^5 - 106053479805 z^6 + 13152093630 z^7 - 1406686905 z^8 + 81601650 z^9) EllipticE[ 2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + 4 Sqrt[1 - z] (111524608 - 2003957800 z + 20107102665 z^2 - 190868267590 z^3 - 2639773676435 z^4 - 2491726929090 z^5 - 106053479805 z^6 + 13152093630 z^7 - 1406686905 z^8 + 81601650 z^9) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + (446098432 - 8294642720 z + 85392562645 z^2 - 812940333010 z^3 + 19021293706835 z^4 + 50926581782720 z^5 + 17966201175195 z^6 - 904956021450 z^7 + 111326201805 z^8 - 11612542500 z^9 + 652813200 z^10) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])]))/ (953912281011765075 Pi Sqrt[Sqrt[2] + Sqrt[1 - Sqrt[1 - z]]] 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]