Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b940)

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=13/8

http://functions.wolfram.com/07.23.03.b940.01

Input Form

Hypergeometric2F1[-(41/8), 13/8, 6, z] == (1/(7036938400216725 Pi z^5)) (262144 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (-4 (114196480 - 970224000 z + 3480103575 z^2 - 6412521975 z^3 + 4129829550 z^4 - 31538163726 z^5 + 40372174035 z^6 - 29467456155 z^7 + 13101014520 z^8 - 3315626160 z^9 + 368254656 z^10) EllipticE[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 10 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (7137280 - 59468040 z + 208106775 z^2 - 369427425 z^3 - 2477897730 z^4 + 3242774574 z^5 - 2397386997 z^6 + 1076107275 z^7 - 274475520 z^8 + 30687888 z^9) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 3 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] Sqrt[1 - z] (-14274560 + 110906640 z - 355438635 z^2 + 550643940 z^3 - 9085625010 z^4 + 12236344812 z^5 - 9212336523 z^6 + 4197173112 z^7 - 1084750128 z^8 + 122751552 z^9) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 2 (114196480 - 970224000 z + 3480103575 z^2 - 6412521975 z^3 + 4129829550 z^4 - 31538163726 z^5 + 40372174035 z^6 - 29467456155 z^7 + 13101014520 z^8 - 3315626160 z^9 + 368254656 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]