We represent the Generalized Incomplete Gamma Function as a sum of Modified Bessel Functions valid for non-integer α. For integer values of α we derive the corresponding limit case. Moreover, we discuss numerical techniques to evaluate this function.
Asymptotics of the modified bessel and the incomplete gamma matrix functions
✍ Scribed by J. Sastre; L. Jódar
- Publisher
- Elsevier Science
- Year
- 2003
- Tongue
- English
- Weight
- 352 KB
- Volume
- 16
- Category
- Article
- ISSN
- 0893-9659
No coin nor oath required. For personal study only.
✦ Synopsis
thii paper, an asymptotic expression of the incomplete gamma matrix function and integral expressions of Bessel matrix functions are given. Results are applied to study the asymptotic behavior of the modified Bessel function.
📜 SIMILAR VOLUMES
A general expression for the operational matrix of integration P for the case of Bessel functions is derived. Using this P, several problems such as identiJication, analysis and optimal control may be studied. Examples are included to illustrate the theoretical results.
Ahstrati-A method to compute the modified Bessel functions Z,(x) and K.(x) for positive real x and integer a is presented. A recursion procedure is used, based on Miller's algorithm.
apparently new expansion of the exponential integral El in incomplete gamma functions is presented and shown to be a limiting csse of a more general expansion given by Mcomi in 1950 without proof. This latter expansion is proved here by interpreting it as a "multiplication theorem". A companion resu