Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a7sa)

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=5

http://functions.wolfram.com/07.23.03.a7sa.01

Input Form

Hypergeometric2F1[-(23/4), 5, 23/4, z] == (1/(11123294208 z^(19/4))) (4 z^(3/4) (1850695 + 1692064 z + 3263953 z^2 + 11036872 z^3 + 2866242286 z^4 - 15714668120 z^5 + 36014436426 z^6 - 44391204648 z^7 + 31022210043 z^8 - 11641208040 z^9 + 1830673845 z^10) - 100947 (1 - z)^(13/2) (55 + 396 z + 1674 z^2 + 5580 z^3 + 18135 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]