Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b4p0)

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.b4p0.01

Input Form

Hypergeometric2F1[-(47/8), -(35/8), 6, z] == (524288 2^(1/4) (2 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (813683539968 - 20472405003648 z + 279235764400905 z^2 - 3028955849585640 z^3 + 38173602225393180 z^4 + 1375812754447184232 z^5 + 4185025478048148118 z^6 + 3630824762538867240 z^7 + 982451828104069980 z^8 + 64572096027550040 z^9 + 23236414014825 z^10) 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) (813683539968 - 20472405003648 z + 279235764400905 z^2 - 3028955849585640 z^3 + 38173602225393180 z^4 + 1375812754447184232 z^5 + 4185025478048148118 z^6 + 3630824762538867240 z^7 + 982451828104069980 z^8 + 64572096027550040 z^9 + 23236414014825 z^10) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - Sqrt[1 - z] (813683539968 - 20472405003648 z + 279235764400905 z^2 - 3028955849585640 z^3 + 38173602225393180 z^4 + 1375812754447184232 z^5 + 4185025478048148118 z^6 + 3630824762538867240 z^7 + 982451828104069980 z^8 + 64572096027550040 z^9 + 23236414014825 z^10) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - (813683539968 - 20777536331136 z + 286829481929913 z^2 - 3131614364516820 z^3 + 39281914297742220 z^4 - 952336520952792888 z^5 - 6067268156502735194 z^6 - 8889079306772989488 z^7 - 4108940680807829460 z^8 - 555240396617659240 z^9 - 11873807561575575 z^10 + 92945656059300 z^11) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))/ (606635362509890935896675 Pi (1 + Sqrt[1 - z])^(1/4) z^5)

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]