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.Comment: 21 pages, 6 figures. To appear in "Archives of Inequalities and
Applications
