Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b9kc)

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.b9kc.01

Input Form

Hypergeometric2F1[-(41/8), 43/8, 6, z] == (524288 2^(1/4) (-2 Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z] (114196480 + 117319040 z + 239220855 z^2 + 753125925 z^3 + 4451895825 z^4 - 285559677117 z^5 + 1177770685104 z^6 - 2054818950912 z^7 + 1839474524160 z^8 - 836926504960 z^9 + 154103971840 z^10) EllipticE[1/2 - Sqrt[1 - z]/ (Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] + (114196480 + 74495360 z + 183516615 z^2 + 645167595 z^3 + 4134482025 z^4 - 99420007167 z^5 + 359981087076 z^6 - 583452020736 z^7 + 495668339712 z^8 - 216455249920 z^9 + 38525992960 z^10) EllipticK[1/2 - Sqrt[1 - z]/ (Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] + Sqrt[1 - z] (114196480 + 117319040 z + 239220855 z^2 + 753125925 z^3 + 4451895825 z^4 - 285559677117 z^5 + 1177770685104 z^6 - 2054818950912 z^7 + 1839474524160 z^8 - 836926504960 z^9 + 154103971840 z^10) EllipticK[1/2 - Sqrt[1 - z]/ (Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] + Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z] (114196480 + 117319040 z + 239220855 z^2 + 753125925 z^3 + 4451895825 z^4 - 285559677117 z^5 + 1177770685104 z^6 - 2054818950912 z^7 + 1839474524160 z^8 - 836926504960 z^9 + 154103971840 z^10) EllipticK[1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])]))/ (49258568801517075 Pi (1 + Sqrt[1 - z])^(1/4) (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]