Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b6np)

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=7/8

http://functions.wolfram.com/07.23.03.b6np.01

Input Form

Hypergeometric2F1[-(45/8), 7/8, 19/4, z] == (1/(18941609865 z^4)) (8 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (4 (-2148146 + 21188531 z - 95731987 z^2 + 276399435 z^3 - 83041684 z^4 + 73409813 z^5 - 44996303 z^6 + 18061141 z^7 - 4276160 z^8 + 453376 z^9) + (1/Sqrt[1 - z]) (8592584 - 89050416 z + 424230937 z^2 - 1287004485 z^3 + 2025911714 z^4 - 2087002106 z^5 + 1648340333 z^6 - 913287841 z^7 + 335420960 z^8 - 73405696 z^9 + 7254016 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]