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

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=-35/8, b>=a

For fixed z and a=-35/8, b=-31/8

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

Input Form

Hypergeometric2F1[-(35/8), -(31/8), 6, z] == (524288 2^(1/4) (2 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (1331724288 - 27263933568 z + 295685830755 z^2 - 2478861827715 z^3 + 23308749619155 z^4 + 555208018551237 z^5 + 1067497207727713 z^6 + 512404440892815 z^7 + 59178087676905 z^8 + 771874445615 z^9) 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) (1331724288 - 27263933568 z + 295685830755 z^2 - 2478861827715 z^3 + 23308749619155 z^4 + 555208018551237 z^5 + 1067497207727713 z^6 + 512404440892815 z^7 + 59178087676905 z^8 + 771874445615 z^9) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - Sqrt[1 - z] (1331724288 - 27263933568 z + 295685830755 z^2 - 2478861827715 z^3 + 23308749619155 z^4 + 555208018551237 z^5 + 1067497207727713 z^6 + 512404440892815 z^7 + 59178087676905 z^8 + 771874445615 z^9) EllipticK[1/2 - (1 - z)^(1/4)/ (Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + (-1331724288 + 27763330176 z - 305773252083 z^2 + 2587020940245 z^3 - 24209441150895 z^4 + 463389892849833 z^5 + 1918104613972679 z^6 + 1671236997942783 z^7 + 384254456606235 z^8 + 17234341899715 z^9) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))/ (264790642736748553425 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]