Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.be4n)

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=-33/8, b>=a

For fixed z and a=-33/8, b=13/8

http://functions.wolfram.com/07.23.03.be4n.01

Input Form

Hypergeometric2F1[-(33/8), 13/8, 5, z] == (1/(1983465358875 Pi z^4)) (32768 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (8 (391680 - 2501040 z + 6059565 z^2 - 4476780 z^3 + 35575030 z^4 - 43576956 z^5 + 27762933 z^6 - 9386608 z^7 + 1334256 z^8) EllipticE[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 5 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (97920 - 609195 z + 1419840 z^2 + 11191950 z^3 - 14049740 z^4 + 9079701 z^5 - 3102396 z^6 + 444752 z^7) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 3 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] Sqrt[1 - z] (-97920 + 554115 z - 1119195 z^2 + 20518575 z^3 - 26614345 z^4 + 17569794 z^5 - 6109488 z^6 + 889504 z^7) EllipticK[ 1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 4 (391680 - 2501040 z + 6059565 z^2 - 4476780 z^3 + 35575030 z^4 - 43576956 z^5 + 27762933 z^6 - 9386608 z^7 + 1334256 z^8) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))

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]