Some Upper Bounds for RKHS Approximation by Bessel Functions

Uniform Bounds for Bessel Functions

For ν > −1/2 and x real we shall establish explicit bounds for the Bessel function Jν(x) which are uniform in x and ν. This work and the recent result of L. J. Landau [7] provide relatively sharp inequalities for all real x.

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...

Some Distributions Involving Bessel Functions

Some Inequalities for Modified Bessel Functions

We denote by Iν and Kν the Bessel functions of the first and third kind, respectively. Motivated by the relevance of the function wν t t Iν−1 t /Iν t , t > 0, in many contexts of applied mathematics and, in particular, in some elasticity problems Simpson and Spector 1984 , we establish new inequalities for Iν t /Iν−1 t . The results are based on the recurrence relations for Iν and Iν−1 and the ...

Lower Bounds for Approximation of Some Classes of Lebesgue Measurable Functions by Sigmoidal Neural Networks

We propose a general method for estimating the distance between a compact subspace K of the space L([0, 1]) of Lebesgue measurable functions defined on the hypercube [0, 1], and the class of functions computed by artificial neural networks using a single hidden layer, each unit evaluating a sigmoidal activation function. Our lower bounds are stated in terms of an invariant that measures the osc...