Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b4oh)

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=-47/8, b>=a

For fixed z and a=-47/8, b=-35/8

http://functions.wolfram.com/07.23.03.b4oh.01

Input Form

Hypergeometric2F1[-(47/8), -(35/8), 5/4, z] == (1/(26175835 z)) (2^(1/4) (1 + Sqrt[1 - z])^(3/4) (5730381 + 221910778 z + 1243780187 z^2 + 1798709964 z^3 + 730047283 z^4 + 64285466 z^5 - 183483 z^6 + (1/Sqrt[1 - z]) (-5730381 - 205957670 z - 867078171 z^2 - 250564536 z^3 + 923944301 z^4 + 387833250 z^5 + 17797851 z^6 - 244644 z^7)))

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]