Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.c9wo)

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=25/8, b>=a

For fixed z and a=25/8, b=45/8

http://functions.wolfram.com/07.23.03.c9wo.01

Input Form

Hypergeometric2F1[25/8, 45/8, -(19/4), z] == (1/(652384 2^(3/4) (-1 + z)^13)) ((1 + Sqrt[1 - z])^(3/4) (-326192 + 5386460 z - 44541303 z^2 + 257384802 z^3 - 1303575897 z^4 - 207945262404 z^5 - 277189974585 z^6 - 63542261646 z^7 - 113702823 z^8 + 3619188 z^9 + (1/Sqrt[1 - z]) (-326192 + 5549556 z - 47193759 z^2 + 279002533 z^3 - 1427024547 z^4 + 226274373945 z^5 + 376957497507 z^6 + 125984218527 z^7 + 5289141663 z^8 - 155725617 z^9 + 4825584 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]