Generating differential equations satisfied by products of functions
โ Scribed by K.C. Chung
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 215 KB
- Volume
- 14
- Category
- Article
- ISSN
- 0893-9659
No coin nor oath required. For personal study only.
โฆ Synopsis
Based on the coefficients of two homogeneous linear differential equations, a method is proposed to construct a third homogeneous linear differential equations which is satisfied by all products of the form uv, where u and v satisfy, respectively, the first and the second given differential equation. The method was used recently in the computation of rapidly oscillatory integrals with kernels which are products of Bessel functions and their variants. (~) 2001 Elsevier Science Ltd. All rights reserved.
๐ SIMILAR VOLUMES
If f is an entire function and satisfies a certain differential equation, then it is shown that f is of bounded index. This extends a theorem of 5. M. Shah.
which are entire functions, for growth problems\_ All such functions, when they satisfy a class of differential equations, are of bounded index and exponential type, and their components are also of bounded index\_