Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b4os)

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=-35/8

http://functions.wolfram.com/07.23.03.b4os.01

Input Form

Hypergeometric2F1[-(47/8), -(35/8), 4, z] == (2048 2^(1/4) (2 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (3178451328 - 102976856697 z + 2577599868753 z^2 + 166919544944231 z^3 + 762406837824905 z^4 + 923861487505677 z^5 + 332443330521547 z^6 + 28036395961477 z^7 + 13872485979 z^8) 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) (3178451328 - 102976856697 z + 2577599868753 z^2 + 166919544944231 z^3 + 762406837824905 z^4 + 923861487505677 z^5 + 332443330521547 z^6 + 28036395961477 z^7 + 13872485979 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - Sqrt[1 - z] (3178451328 - 102976856697 z + 2577599868753 z^2 + 166919544944231 z^3 + 762406837824905 z^4 + 923861487505677 z^5 + 332443330521547 z^6 + 28036395961477 z^7 + 13872485979 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - (3178451328 - 104168775945 z + 2615890274595 z^2 - 91334790439177 z^3 - 933686828645521 z^4 - 1962773166102903 z^5 - 1226348238429335 z^6 - 214961081038115 z^7 - 5784826653243 z^8 + 55489943916 z^9) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))/ (263473276354973685 Pi (1 + Sqrt[1 - z])^(1/4) z^3)

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]