On the expansion of the Kummer function in terms of incomplete Gamma functions

Details On the expansion of the Kummer function in terms of incomplete Gamma functions On the expansion of the Kummer function in terms of incomplete Gamma functions

2003-04-17

arxiv.org/abs/math-ph/0304027v1

Arch. Inequal. Appl. 2 (2004), 49-72

Physics

Mathematical Physics

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

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

On the expansion of the Kummer function in terms of incomplete Gamma functions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On the expansion of the Kummer function in terms of incomplete Gamma functions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the expansion of the Kummer function in terms of incomplete Gamma functions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-10554