Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b58a)

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=13/8

http://functions.wolfram.com/07.23.03.b58a.01

Input Form

Hypergeometric2F1[-(47/8), 13/8, 6, z] == (524288 2^(1/4) (-2 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (14275149824 - 126301618560 z + 472043150865 z^2 - 898751112935 z^3 + 516250024290 z^4 - 1205656756326 z^5 + 1330520243085 z^6 - 901076186835 z^7 + 380360772000 z^8 - 92404350720 z^9 + 9915789312 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) (14275149824 - 126301618560 z + 472043150865 z^2 - 898751112935 z^3 + 516250024290 z^4 - 1205656756326 z^5 + 1330520243085 z^6 - 901076186835 z^7 + 380360772000 z^8 - 92404350720 z^9 + 9915789312 z^10) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + Sqrt[1 - z] (14275149824 - 126301618560 z + 472043150865 z^2 - 898751112935 z^3 + 516250024290 z^4 - 1205656756326 z^5 + 1330520243085 z^6 - 901076186835 z^7 + 380360772000 z^8 - 92404350720 z^9 + 9915789312 z^10) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + (14275149824 - 131654799744 z + 517942497345 z^2 - 1063594067705 z^3 + 811250038170 z^4 + 3956843486574 z^5 - 7058140139259 z^6 + 6905462709915 z^7 - 4296109348080 z^8 + 1694333773440 z^9 - 388622665728 z^10 + 39663157248 z^11) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))/ (1385566795817088885 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]