Polynomial approximations to Bessel functions

Polynomial Approximations to Bessel Functions

A polynomial approximation to Bessel functions that arises from an electromagnetic scattering problem is examined. The approximation is extended to Bessel functions of any integer order, and the relationship to the Taylor series is derived. Numerical calculations show that the polynomial approximation and the Taylor series truncated to the same order have similar accuracies.

On Polynomial Approximations to AC

We make progress on some questions related to polynomial approximations of AC0. It is known, by works of Tarui (Theoret. Comput. Sci. 1993) and Beigel, Reingold, and Spielman (Proc. 6th CCC 1991), that any AC0 circuit of size s and depth d has an ε-error probabilistic polynomial over the reals of degree (log(s/ε))O(d). We improve this upper bound to (log s)O(d) · log(1/ε), which is much better ...

Some Integrals Involving Bessel Functions Some Integrals Involving Bessel Functions

A number of new definite integrals involving Bessel functions are presented. These have been derived by finding new integral representations for the product of two Bessel functions of different order and argument in terms of the generalized hypergeometric function with subsequent reduction to special cases. Connection is made with Weber's second exponential integral and Laplace transforms of pr...

Noncommutative Bessel Symmetric Functions

The consideration of tensor products of 0-Hecke algebra modules leads to natural analogs of the Bessel J-functions in the algebra of noncommutative symmetric functions. This provides a simple explanation of various combinatorial properties of Bessel functions.

Extension of Oppenheim’s Problem to Bessel Functions