Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b70u)

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=-45/8, b>=a

For fixed z and a=-45/8, b=31/8

http://functions.wolfram.com/07.23.03.b70u.01

Input Form

Hypergeometric2F1[-(45/8), 31/8, -(7/2), -z] == (1/(41216 (1 + z)^(11/8))) ((41216 - 211600 z + 879681 z^2 - 4230804 z^3 + 43524096 z^4 + 582945792 z^5 + 1171456000 z^6 + 637272064 z^7) Cos[(3 ArcTan[Sqrt[z]])/4] - Sqrt[z] (-30912 + 163208 z - 684595 z^2 + 3278880 z^3 + 335219456 z^4 + 808890368 z^5 + 477954048 z^6) Sin[(3 ArcTan[Sqrt[z]])/4])

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]