Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b587)

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=13/8

http://functions.wolfram.com/07.23.03.b587.01

Input Form

Hypergeometric2F1[-(47/8), 13/8, 21/4, z] == (1/(20689636275 z^5)) (16 2^(1/4) (1 + Sqrt[1 - z])^(3/4) (-6970288 + 58309140 z - 198150543 z^2 + 286753627 z^3 + 640395210 z^4 - 1339651782 z^5 + 1488097285 z^6 - 1031698521 z^7 + 447388704 z^8 - 111668480 z^9 + 12300288 z^10 + (1/Sqrt[1 - z]) (6970288 - 61794284 z + 226433827 z^2 - 378975899 z^3 - 518415170 z^4 + 2331947422 z^5 - 3444010161 z^6 + 3141633849 z^7 - 1880438448 z^8 + 723148160 z^9 - 162899968 z^10 + 16400384 z^11)))

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]