Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b5ht)

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=29/8

http://functions.wolfram.com/07.23.03.b5ht.01

Input Form

Hypergeometric2F1[-(47/8), 29/8, 6, z] == (524288 2^(1/4) (-2 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (1098088448 - 3744653184 z + 1418822229 z^2 + 2481556572 z^3 + 8282913870 z^4 - 77392420644 z^5 + 174939167557 z^6 - 198045679392 z^7 + 125243990784 z^8 - 42501550080 z^9 + 6066339840 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) (1098088448 - 3744653184 z + 1418822229 z^2 + 2481556572 z^3 + 8282913870 z^4 - 77392420644 z^5 + 174939167557 z^6 - 198045679392 z^7 + 125243990784 z^8 - 42501550080 z^9 + 6066339840 z^10) EllipticK[1/2 - (1 - z)^(1/4)/ (Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + Sqrt[1 - z] (1098088448 - 3744653184 z + 1418822229 z^2 + 2481556572 z^3 + 8282913870 z^4 - 77392420644 z^5 + 174939167557 z^6 - 198045679392 z^7 + 125243990784 z^8 - 42501550080 z^9 + 6066339840 z^10) EllipticK[1/2 - (1 - z)^(1/4)/ (Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + (1098088448 - 4156436352 z + 2710470213 z^2 + 2273654328 z^3 + 7371682758 z^4 + 135641027676 z^5 - 581889804419 z^6 + 1034199766116 z^7 - 1015430575104 z^8 + 579856966656 z^9 - 181633351680 z^10 + 24265359360 z^11) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))/ (56719108600699545 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]