Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b5lf)

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=37/8

http://functions.wolfram.com/07.23.03.b5lf.01

Input Form

Hypergeometric2F1[-(47/8), 37/8, -(23/4), z] == (1/(62452544 2^(3/4) (-1 + z)^4)) ((1 + Sqrt[1 - z])^(3/4) (2 (15613136 + 14255472 z + 15021391 z^2 + 18328464 z^3 + 27764919 z^4 + 60775242 z^5 - 6541113216 z^6 + 16367104512 z^7 - 14191558656 z^8 + 4191289344 z^9) + (1/Sqrt[1 - z]) (31226272 + 12897808 z + 11884026 z^2 + 16120027 z^3 + 30444316 z^4 + 85358223 z^5 + 14145752016 z^6 - 53656720128 z^7 + 75597299712 z^8 - 47390982144 z^9 + 11176771584 z^10)))

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]