Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b5l0)

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=35/8

http://functions.wolfram.com/07.23.03.b5l0.01

Input Form

Hypergeometric2F1[-(47/8), 35/8, 5, z] == (65536 2^(1/4) (-4 Sqrt[1 - z] (223049216 + 397306416 z + 1083444141 z^2 + 5888586431 z^3 - 138947285637 z^4 + 490497028665 z^5 - 781110154720 z^6 + 655230011280 z^7 - 283439819520 z^8 + 50082489600 z^9) EllipticE[ 2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - 2 Sqrt[2 - 2 Sqrt[1 - z]] Sqrt[1 - z] (223049216 + 397306416 z + 1083444141 z^2 + 5888586431 z^3 - 138947285637 z^4 + 490497028665 z^5 - 781110154720 z^6 + 655230011280 z^7 - 283439819520 z^8 + 50082489600 z^9) EllipticE[ 2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + 2 Sqrt[1 - z] (223049216 + 397306416 z + 1083444141 z^2 + 5888586431 z^3 - 138947285637 z^4 + 490497028665 z^5 - 781110154720 z^6 + 655230011280 z^7 - 283439819520 z^8 + 50082489600 z^9) EllipticK[ 2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + (446098432 + 515801312 z + 1624512747 z^2 + 10319947027 z^3 + 200495898101 z^4 - 1367918617215 z^5 + 3417518933500 z^6 - 4438576252240 z^7 + 3219947228160 z^8 - 1243940755200 z^9 + 200329958400 z^10) EllipticK[ 2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])]))/ (15926055124334355 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]