Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b5b7)

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=19/8

http://functions.wolfram.com/07.23.03.b5b7.01

Input Form

Hypergeometric2F1[-(47/8), 19/8, 5, z] == (65536 2^(1/4) (-16 Sqrt[1 - z] (12868224 - 61794284 z + 63168235 z^2 + 121980040 z^3 - 810055840 z^4 + 1533959198 z^5 - 1542875443 z^6 + 895003590 z^7 - 284161800 z^8 + 38454000 z^9) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - 8 Sqrt[2 - 2 Sqrt[1 - z]] Sqrt[1 - z] (12868224 - 61794284 z + 63168235 z^2 + 121980040 z^3 - 810055840 z^4 + 1533959198 z^5 - 1542875443 z^6 + 895003590 z^7 - 284161800 z^8 + 38454000 z^9) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + 8 Sqrt[1 - z] (12868224 - 61794284 z + 63168235 z^2 + 121980040 z^3 - 810055840 z^4 + 1533959198 z^5 - 1542875443 z^6 + 895003590 z^7 - 284161800 z^8 + 38454000 z^9) EllipticK[ 2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + (102945792 - 558695392 z + 803761335 z^2 + 705741660 z^3 + 7089832730 z^4 - 24114430476 z^5 + 36606230871 z^6 - 32040447400 z^7 + 16745311440 z^8 - 4884984000 z^9 + 615264000 z^10) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])]))/ (465674126442525 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]