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

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=47/8

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

Input Form

Hypergeometric2F1[-(37/8), 47/8, 5/2, -z] == (16 (Sqrt[z] (-183483 + 47891675 z + 687475216 z^2 + 3079303424 z^3 + 5954682880 z^4 + 5208473600 z^5 + 1693450240 z^6) Cos[(3 ArcTan[Sqrt[z]])/4] - 2 (-122322 + 6544227 z + 166937970 z^2 + 917766784 z^3 + 1982896640 z^4 + 1860567040 z^5 + 635043840 z^6) Sin[(3 ArcTan[Sqrt[z]])/4]))/(608777225 z^(3/2) (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]