Some Properties of Convolution Sequences and Asymptotics for the Taylor Coefficients for Products of Bessel Functions

Let {a_n}, {b_n} be sequences of real numbers. We define the convolution of {a_n} and {b_n} to be the sequence {c_n} defined by (1) { a n ∗ b n } n : = c n = ∑ k = 0 n a k b n − k ,   n = 0 , 1 , 2 … … https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003072584/300cbf75-7783-4a6f-9796-7cd4d736d320/content/eq2575.tif"/>