How to compute multivariate Bessel expansions. (English) Zbl 07887391
Bessel functions and products of Bessel functions are particularly important in many fields of pure and applied mathematics, for instance when multivariate Hankel transforms have to be computed. In this paper the authors attempt successfully to provide methods for computations of products and tensor products of Bessel functions of the first kind.
Their algorithms allow explicit expressions for certain sums of Bessel functions using zeros of the Bessel functions. More explicit formulae are provided for cases when sums of Bessel functions are given as polynomials. Those results are then generalised to series of Bessel functions times certain coefficients multiplied by even powers.
Reviewer: Martin D. Buhmann (Gießen)
MSC:
| 33C10 | Bessel and Airy functions, cylinder functions, \({}_0F_1\) |
| 41A58 | Series expansions (e.g., Taylor, Lidstone series, but not Fourier series) |
| 41A63 | Multidimensional problems |
| 44A20 | Integral transforms of special functions |
Software:
DLMFReferences:
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