Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bb89)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 8 and fixed z and a<0

For fixed z and a=-37/8, b>=a

For fixed z and a=-37/8, b=-33/8

http://functions.wolfram.com/07.23.03.bb89.01

Input Form

Hypergeometric2F1[-(37/8), -(33/8), 11/2, -z] == -((1024 (Sqrt[z] (-1344 - 30152 z - 372921 z^2 - 3909087 z^3 - 443250093 z^4 + 1913277717 z^5 - 2105990859 z^6 + 710717987 z^7 - 63216591 z^8 + 669231 z^9) Cos[(3 ArcTan[Sqrt[z]])/4] + (1792 + 40464 z + 503031 z^2 + 5283313 z^3 + 90702339 z^4 - 1128904491 z^5 + 2331409093 z^6 - 1421461293 z^7 + 256341249 z^8 - 9557993 z^9) Sin[(3 ArcTan[Sqrt[z]])/4]))/ (384800166023 z^(9/2) (1 + z)^(3/8)))

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]