Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b9jw)

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.b9jw.01

Input Form

Hypergeometric2F1[-(41/8), 43/8, 11/4, z] == (2 2^(3/4) (-10455 + 25914875 z - 249201140 z^2 + 835855872 z^3 - 1282159616 z^4 + 923598848 z^5 - 254017536 z^6 + (1/Sqrt[1 - z]) (10455 + 26608390 z - 300136365 z^2 + 1245039312 z^3 - 2539552512 z^4 + 2750103552 z^5 - 1520762880 z^6 + 338690048 z^7)))/ (105056985 (1 + Sqrt[1 - z])^(3/4) 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]