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

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=15/4, b>=a

For fixed z and a=15/4, b=21/4

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

Input Form

Hypergeometric2F1[15/4, 21/4, -(11/2), -z] == (1/(2112 Sqrt[2] Sqrt[-1 + Sqrt[1 + z]])) (Sqrt[z] ((1/(1 + z)^(29/2)) (1056 + 18960 z + 168306 z^2 + 1010599 z^3 + 4873385 z^4 + 23021427 z^5 + 1288201505 z^6 - 2445415147 z^7 + 1027742187 z^8 - 90578815 z^9 - 59015 z^10) + (1/(1 + z)^14) (2 (528 + 9216 z + 79611 z^2 + 466613 z^3 + 2212782 z^4 + 10458019 z^5 - 459589926 z^6 + 583093067 z^7 - 151582330 z^8 + 5370365 z^9 + 59015 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]