Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.cdm4)

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=45/8

http://functions.wolfram.com/07.23.03.cdm4.01

Input Form

Hypergeometric2F1[41/8, 45/8, -(19/4), z] == (1/(7176224 2^(3/4) (-1 + z)^15)) ((1 + Sqrt[1 - z])^(3/4) (-3588112 + 74925444 z - 807360609 z^2 + 6314775607 z^3 - 45439272021 z^4 - 15747856850565 z^5 - 41902339950915 z^6 - 28493523339579 z^7 - 5456181066807 z^8 - 211066687419 z^9 + (1/Sqrt[1 - z]) (-3588112 + 76719500 z - 844374817 z^2 + 6709314488 z^3 - 48500282428 z^4 + 16701428219744 z^5 + 51548963806650 z^6 + 42517625538216 z^7 + 10980794954772 z^8 + 755318126388 z^9 + 6202785567 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]