منابع مشابه
On some expansions for the Euler Gamma function and the Riemann Zeta function
Abstract In the present paper we introduce some expansions, based on the falling factorials, for the Euler Gamma function and the Riemann Zeta function. In the proofs we use the Faá di Bruno formula, Bell polynomials, potential polynomials, Mittag-Leffler polynomials, derivative polynomials and special numbers (Eulerian numbers and Stirling numbers of both kinds). We investigate the rate of con...
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In this paper, we develop the Windschitl and Smith formulas for the gamma function to complete asymptotic expansions and provide explicit formulas for determining the coefficients of these asymptotic expansions. Furthermore, we establish new asymptotic expansions for the ratio of gamma functions Γ(x + 1)/Γ(x + 1 2 ).
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In a recent paper in this journal, Gautschi et al. [W. Gautschi, F.E. Harris, N.M. Temme, Expansions of the exponential integral in incomplete Gamma functions, Appl. Math. Lett. 16 (2003) 1095–1099] presented an interesting expansion formula for the exponential integral E1(z) in a series of the incomplete Gamma function γ (α, z). Their investigation was motivated by a search for better methods ...
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We study weak-coupling perturbation expansions for the ground-state energy of the Hamiltonian with the generalized spiked harmonic oscillator potential V (x) = Bx + A x + λ x , and also for the bottoms of the angular momentum subspaces labelled by l = 0, 1, . . . , in N -dimensions corresponding to the spiked harmonic oscillator potential V (x) = x + λ x , where α is a real positive parameter. ...
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A necessary and sufficient condition in terms of lower cut sets are given for the insertion of a $gamma-$continuous function between two comparable real-valued functions.
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ژورنال
عنوان ژورنال: SIAM Review
سال: 1984
ISSN: 0036-1445,1095-7200
DOI: 10.1137/1026049