Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.9828)

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=-23/4, b>=a

For fixed z and a=-23/4, b=3

http://functions.wolfram.com/07.23.03.9828.01

Input Form

Hypergeometric2F1[-(23/4), 3, 23/4, z] == (1/(1216610304 z^(19/4))) (4 z^(3/4) (1850695 - 8671828 z + 9993753 z^2 + 6460608 z^3 + 320745558 z^4 - 1082240712 z^5 + 1663380194 z^6 - 1466460128 z^7 + 768451827 z^8 - 224102340 z^9 + 28164213 z^10) - 100947 (1 - z)^(17/2) (55 + 198 z + 279 z^2) 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]