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

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=-11/4, b>=a

For fixed z and a=-11/4, b=-9/4

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

Input Form

Hypergeometric2F1[-(11/4), -(9/4), 11/2, -z] == (16 Sqrt[2] (-112 - 1580 z - 11447 z^2 - 63723 z^3 - 504438 z^4 + 2373470 z^5 - 1357555 z^6 + 118057 z^7 + (1/Sqrt[1 + z]) (112 + 1636 z + 12223 z^2 + 69256 z^3 + 534963 z^4 - 815716 z^5 - 873291 z^6 + 407032 z^7 - 11799 z^8)))/ (42010995 z^(9/2) 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]