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

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 4 and fixed z

For fixed z and a=9/4, b>=a

For fixed z and a=9/4, b=5

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

Input Form

Hypergeometric2F1[9/4, 5, -(21/4), z] == (1/(3808 (-1 + z)^13)) (4 (-952 + 14416 z - 105456 z^2 + 506512 z^3 - 1881440 z^4 + 6602224 z^5 - 53672592 z^6 + 234023 z^7 + 44860210 z^8 + 3629780 z^9 - 194810 z^10 + 8085 z^11) - 231 Sqrt[1 - z] z^(25/4) (483923 + 333740 z + 15170 z^2 - 820 z^3 + 35 z^4) Beta[z, 3/4, 1/2])

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]