Data di Pubblicazione:
2004
Citazione:
On the expansion of the Kummer function in terms of incomplete gamma functions / C. Morosi, L. Pizzocchero. - In: ARCHIVES OF INEQUALITIES AND APPLICATIONS. - ISSN 1542-6149. - 2:1(2004), pp. 49-72.
Abstract:
The expansion of Kummer's hypergeometric
function as a series of incomplete Gamma functions is discussed,
for real values of the parameters and of the variable. The error performed
approximating the Kummer function with a finite sum of Gammas is evaluated
analytically. Bounds for it are derived, both pointwisely and uniformly in
the variable; these characterize the convergence rate of the series,
both pointwisely and in appropriate sup norms.
The same analysis shows that finite sums of very few Gammas
are sufficiently close to the Kummer
function.
The combination of these results with the known approximation methods
for the incomplete Gammas allows to construct upper and lower
approximants for the Kummer function using only exponentials, real powers and rational functions.
Illustrative examples are provided.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
Approximations and expansions; Confluent hypergeometric function; Inequalities in approximation
Elenco autori:
C. Morosi, L. Pizzocchero
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