Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b980)

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=-41/8, b>=a

For fixed z and a=-41/8, b=21/8

http://functions.wolfram.com/07.23.03.b980.01

Input Form

Hypergeometric2F1[-(41/8), 21/8, 6, z] == (1/(3388155526030275 Pi z^5)) (262144 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (-4 (-114196480 + 681164160 z - 1405497015 z^2 + 673009260 z^3 + 825965910 z^4 - 16194555684 z^5 + 32760173673 z^6 - 32673823632 z^7 + 18419594688 z^8 - 5646571392 z^9 + 736509312 z^10) EllipticE[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 24 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] Sqrt[1 - z] (1784320 - 9346770 z + 15295665 z^2 - 550643940 z^4 + 1208063016 z^5 - 1258113861 z^6 + 731863242 z^7 - 230159160 z^8 + 30687888 z^9) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 5 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (-14274560 + 82803600 z - 162815715 z^2 + 61182660 z^3 - 2477897730 z^4 + 5202882252 z^5 - 5285614275 z^6 + 3017125368 z^7 - 933788592 z^8 + 122751552 z^9) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 2 (-114196480 + 681164160 z - 1405497015 z^2 + 673009260 z^3 + 825965910 z^4 - 16194555684 z^5 + 32760173673 z^6 - 32673823632 z^7 + 18419594688 z^8 - 5646571392 z^9 + 736509312 z^10) 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]