Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b5mn)

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=-47/8, b>=a

For fixed z and a=-47/8, b=37/8

http://functions.wolfram.com/07.23.03.b5mn.01

Input Form

Hypergeometric2F1[-(47/8), 37/8, 17/4, z] == (1/(75555486545 z^4)) (8 2^(1/4) (1 + Sqrt[1 - z])^(3/4) (4 (603198 + 3250567 z + 25300805 z^2 + 827386590 z^3 - 7002948573 z^4 + 21095421237 z^5 - 32128126272 z^6 + 26756108544 z^7 - 11673108480 z^8 + 2095644672 z^9) + (1/Sqrt[1 - z]) (-2412792 - 11795872 z - 94400487 z^2 - 3257168667 z^3 + 34402342675 z^4 - 129633627465 z^5 + 255076688592 z^6 - 291356203776 z^7 + 195503210496 z^8 - 71803404288 z^9 + 11176771584 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]