Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b7ks)

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=-43/8, b>=a

For fixed z and a=-43/8, b=-15/8

http://functions.wolfram.com/07.23.03.b7ks.01

Input Form

Hypergeometric2F1[-(43/8), -(15/8), 6, z] == (524288 2^(1/4) (-2 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (-1686601728 + 29522118528 z - 266572169325 z^2 + 1794165309090 z^3 - 12859530338655 z^4 - 196853255818972 z^5 - 204609064242523 z^6 - 27639670728670 z^7 + 1458256130695 z^8 - 107464415240 z^9 + 4879201600 z^10) EllipticE[1/2 - (1 - z)^(1/4)/ (Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + (-1686601728 + 30154594176 z - 277470021213 z^2 + 1891194577965 z^3 - 13506556323645 z^4 + 201404146869173 z^5 + 500824418656529 z^6 + 187393023586463 z^7 + 369492788665 z^8 - 27094816385 z^9 + 1219800400 z^10) EllipticK[1/2 - (1 - z)^(1/4)/ (Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (-1686601728 + 29522118528 z - 266572169325 z^2 + 1794165309090 z^3 - 12859530338655 z^4 - 196853255818972 z^5 - 204609064242523 z^6 - 27639670728670 z^7 + 1458256130695 z^8 - 107464415240 z^9 + 4879201600 z^10) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + Sqrt[1 - z] (-1686601728 + 29522118528 z - 266572169325 z^2 + 1794165309090 z^3 - 12859530338655 z^4 - 196853255818972 z^5 - 204609064242523 z^6 - 27639670728670 z^7 + 1458256130695 z^8 - 107464415240 z^9 + 4879201600 z^10) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))/ (103181330268310469175 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]