Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b4ow)

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.b4ow.01

Input Form

Hypergeometric2F1[-(47/8), -(35/8), 5, z] == (65536 2^(1/4) (2 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (-76282831872 + 2077912555680 z - 33737150156385 z^2 + 564988719765015 z^3 + 26323417857879307 z^4 + 96196322749664627 z^5 + 97304272814507325 z^6 + 30062731903141445 z^7 + 2221228879535065 z^8 + 929456560593 z^9) EllipticE[1/2 - (1 - z)^(1/4)/ (Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (-76282831872 + 2077912555680 z - 33737150156385 z^2 + 564988719765015 z^3 + 26323417857879307 z^4 + 96196322749664627 z^5 + 97304272814507325 z^6 + 30062731903141445 z^7 + 2221228879535065 z^8 + 929456560593 z^9) EllipticK[1/2 - (1 - z)^(1/4)/ (Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - Sqrt[1 - z] (-76282831872 + 2077912555680 z - 33737150156385 z^2 + 564988719765015 z^3 + 26323417857879307 z^4 + 96196322749664627 z^5 + 97304272814507325 z^6 + 30062731903141445 z^7 + 2221228879535065 z^8 + 929456560593 z^9) EllipticK[1/2 - (1 - z)^(1/4)/ (Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 4 (-19070707968 + 526629654408 z - 8627136348675 z^2 + 144357809822460 z^3 - 4110955352035832 z^4 - 32296158376733380 z^5 - 55777992771261558 z^6 - 29641472535952780 z^7 - 4523850122278880 z^8 - 107816961028788 z^9 + 929456560593 z^10) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))/ (1394564051746875714705 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]