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

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=-33/8, b>=a

For fixed z and a=-33/8, b=-21/8

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

Input Form

Hypergeometric2F1[-(33/8), -(21/8), 23/4, z] == (16 2^(3/4) (6600 - 113960 z + 1030485 z^2 - 7213830 z^3 + 1759801579 z^4 + 3724638372 z^5 + 1699513659 z^6 + 154414314 z^7 - 433827 z^8 + (1/Sqrt[1 - z]) (4 (-1650 + 29315 z - 271660 z^2 + 1928810 z^3 + 408024036 z^4 + 303529380 z^5 - 473380860 z^6 - 229300914 z^7 - 10701066 z^8 + 144609 z^9))))/(54326123073 (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]