Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b93b)

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=11/8

http://functions.wolfram.com/07.23.03.b93b.01

Input Form

Hypergeometric2F1[-(41/8), 11/8, 23/4, z] == (16 2^(3/4) (-4 (383350 - 3335145 z + 12451905 z^2 - 24760925 z^3 - 152736516 z^4 + 177346665 z^5 - 123170331 z^6 + 53146629 z^7 - 13187520 z^8 + 1444608 z^9) + (1/Sqrt[1 - z]) (1533400 - 14107280 z + 56286235 z^2 - 122375775 z^3 + 807604614 z^4 - 1604835342 z^5 + 1498643031 z^6 - 896806707 z^7 + 343267680 z^8 - 76914432 z^9 + 7704576 z^10)))/(21991694283 (1 + Sqrt[1 - z])^(3/4) z^4)

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]