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

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=-39/8, b>=a

For fixed z and a=-39/8, b=45/8

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

Input Form

Hypergeometric2F1[-(39/8), 45/8, -(15/4), z] == (1/(1321936 2^(3/4) (-1 + z)^4)) ((1 + Sqrt[1 - z])^(3/4) (4 (165242 + 578347 z + 1915305 z^2 + 7973463 z^3 - 2109452565 z^4 + 8358698304 z^5 - 12528189696 z^6 + 8364195840 z^7 - 2095644672 z^8) + (1/Sqrt[1 - z]) (660968 + 1982904 z + 6421905 z^2 + 27732758 z^3 + 8929026441 z^4 - 47758789584 z^5 + 100359629568 z^6 - 104547041280 z^7 + 54155870208 z^8 - 11176771584 z^9)))

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]