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

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=-35/8, b>=a

For fixed z and a=-35/8, b=23/8

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

Input Form

Hypergeometric2F1[-(35/8), 23/8, 6, z] == (1/(145533329882325 Pi z^5)) (262144 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (4 (20545536 - 101363328 z + 156260313 z^2 - 18802476 z^3 - 33575850 z^4 + 258020220 z^5 - 406919735 z^6 + 306120360 z^7 - 116316720 z^8 + 18033600 z^9) EllipticE[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 3 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] Sqrt[1 - z] (-2568192 + 10804464 z - 11863467 z^2 - 5595975 z^3 + 184667175 z^4 - 337233165 z^5 + 275162680 z^6 - 110906640 z^7 + 18033600 z^8) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 40 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (-321024 + 1531134 z - 2206413 z^2 - 13430340 z^4 + 32692020 z^5 - 35756695 z^6 + 21302190 z^7 - 6762600 z^8 + 901680 z^9) EllipticK[ 1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 2 (20545536 - 101363328 z + 156260313 z^2 - 18802476 z^3 - 33575850 z^4 + 258020220 z^5 - 406919735 z^6 + 306120360 z^7 - 116316720 z^8 + 18033600 z^9) 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]