New series expansions for the confluent hypergeometric function
✍ Scribed by López, José L.; Pérez Sinusía, Ester
- Book ID
- 125449699
- Publisher
- Elsevier Science
- Year
- 2014
- Tongue
- English
- Weight
- 276 KB
- Volume
- 235
- Category
- Article
- ISSN
- 0096-3003
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📜 SIMILAR VOLUMES
An asymptotic expansion of the confluent hypergeometric function U(a,b,x) for large positive 2a-b is given in terms of modified Bessel functions multiplied by Buchholz polynomials, a family of double polynomials in the variables b and x with rational coefficients.
For the confluent hypergeometric functions U (a, b, z) and M (a, b, z) asymptotic expansions are given for a -~ ,o. The expansions contain modified Bessel functions. For real values of the parameters rigorous error bounds are given.
We obtain new and complete asymptotic expansions of the confluent hypergeometric functions M(a, b; z) and U(a, b; z) for large b and z. The expansions are different in the three different regions: The expansions are not of Poincaré type and we give explicit expressions for the terms of the expansio