Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b9k7)

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=43/8

http://functions.wolfram.com/07.23.03.b9k7.01

Input Form

Hypergeometric2F1[-(41/8), 43/8, 5, z] == (65536 2^(1/4) (-2 Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z] (10705920 + 45611680 z + 219886075 z^2 + 1750132150 z^3 - 143378748305 z^4 + 709198155952 z^5 - 1442061001472 z^6 + 1473924874240 z^7 - 753791467520 z^8 + 154103971840 z^9) EllipticE[1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] + 4 (2676480 + 10399240 z + 50420980 z^2 + 415603675 z^3 - 12816778520 z^4 + 55272671233 z^5 - 103744611776 z^6 + 100095993088 z^7 - 48917872640 z^8 + 9631498240 z^9) EllipticK[1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] + Sqrt[1 - z] (10705920 + 45611680 z + 219886075 z^2 + 1750132150 z^3 - 143378748305 z^4 + 709198155952 z^5 - 1442061001472 z^6 + 1473924874240 z^7 - 753791467520 z^8 + 154103971840 z^9) EllipticK[1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] + Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z] (10705920 + 45611680 z + 219886075 z^2 + 1750132150 z^3 - 143378748305 z^4 + 709198155952 z^5 - 1442061001472 z^6 + 1473924874240 z^7 - 753791467520 z^8 + 154103971840 z^9) EllipticK[1/2 - Sqrt[1 - z]/ (Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])]))/ (3040652395155375 Pi (1 + Sqrt[1 - z])^(1/4) (1 - z)^(1/4) z^4)

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]