Naslov
Asymptotic formulae associated with the Wallis power function and digamma function

Autori
Chao-Ping Chen ; Elezović, Neven ; Vukšić, Lenka

Izvornik
Journal of classical analysis (1848-5979) 2 (2013), 2; 151-166

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Gamma function ; digamma (psi) function ; Bernoulli polynomials ; Asymptotic expansions

Sažetak
Let $s, t$ be two given real numbers, $s\not=t$. We determine the coefficients $c_j(s, t)$ such that [\frac{; ; ; ; \Gamma(x+t)}; ; ; ; {; ; ; ; \Gamma(x+s)}; ; ; ; ]^{; ; ; ; 1/(t-s)}; ; ; ; \sim\exp(\psi(x+\sum_{; ; ; ; j=0}; ; ; ; ^{; ; ; ; \infty}; ; ; ; c_j(s, t)x^{; ; ; ; -j}; ; ; ; ))) as $x\to\infty$, where $\psi(x)=\Gamma'(x)/\Gamma(x)$ denotes the digamma function. Also, the analysis of the coefficients in the asymptotic expansion of the composition $\exp(\psi(x+s))$ is given in details.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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