The Use of Special Bilinear Functions in Computing Some Special Funtions

Abstract

In this paper we give, at the beginning, a very quick review of the subject of bilinear functions in connection with the convolution of two n-tuples vectors(originally named quacroms); then we summarize some of its important applications such as the calculation of the product of two polynomials and hence two integers and their use in representing certain quantities. Then we divert our attention towards the main topic of this paper and use these special bilinear functions in computing special functions as in the case of Bernoulli, Hermite, and Legendre polynomials through simple recurrence relations using related linear equations; a related algorithm will then be discussed. Moreover, the first few polynomials of each fore-mentioned ones are computed.