Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a87k)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 4 and fixed z

For fixed z and a=-21/4, b>=a

For fixed z and a=-21/4, b=-17/4

http://functions.wolfram.com/07.23.03.a87k.01

Input Form

Hypergeometric2F1[-(21/4), -(17/4), 6, -z] == (16384 Sqrt[2] ((-(1357824 + 32099808 z + 407370405 z^2 + 4055878632 z^3 + 45981153036 z^4 - 2879277360104 z^5 + 8967541113502 z^6 - 7616551287720 z^7 + 1958835890188 z^8 - 118896017336 z^9 + 195634725 z^10)) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - Sqrt[1 + z] (1357824 + 32099808 z + 407370405 z^2 + 4055878632 z^3 + 45981153036 z^4 - 2879277360104 z^5 + 8967541113502 z^6 - 7616551287720 z^7 + 1958835890188 z^8 - 118896017336 z^9 + 195634725 z^10) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - Sqrt[1 + z] (-1357824 - 31760352 z - 399589437 z^2 - 3959603739 z^3 - 45035823105 z^4 + 1676650876409 z^5 - 4651675403223 z^6 + 3563570270127 z^7 - 816396181291 z^8 + 42061465875 z^9) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] + (1357824 + 32099808 z + 407370405 z^2 + 4055878632 z^3 + 45981153036 z^4 - 2879277360104 z^5 + 8967541113502 z^6 - 7616551287720 z^7 + 1958835890188 z^8 - 118896017336 z^9 + 195634725 z^10) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])]))/ (9940575017748375 Pi z^5 Sqrt[1 + Sqrt[1 + z]])

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]