Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.an84)

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=17/4, b>=a

For fixed z and a=17/4, b=23/4

http://functions.wolfram.com/07.23.03.an84.01

Input Form

Hypergeometric2F1[17/4, 23/4, -(11/2), -z] == (1/(704 Sqrt[2] Sqrt[-1 + Sqrt[1 + z]])) (Sqrt[z] ((1/(1 + z)^15) (352 + 6800 z + 65742 z^2 + 437203 z^3 + 2392845 z^4 + 13329615 z^5 - 799144595 z^6 + 1372808857 z^7 - 554914377 z^8 + 48462325 z^9 - 27807 z^10) + (1/(1 + z)^(31/2)) (2 (176 + 3488 z + 34549 z^2 + 234623 z^3 + 1301820 z^4 + 7237620 z^5 + 540957470 z^6 - 1326327686 z^7 + 795863948 z^8 - 126715180 z^9 + 2975349 z^10 + 27807 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]