Chapter 50  Integer Sequences and Orthogonal Polynomials

Our previous chapters have demonstrated that various functions can be used to express integer sequences or linear recurrences.  The intersystem polynomials (ISP) were shown to be equivalent to Bell Polynomials for sequence numbers of polynomials of any degree.  Binomial coefficients and the incomplete Beta function could be developed to calculate Perrin numbers. These equations lead to expressions of sequence numbers using the hypergeometric functions and  the specialized form of the Jacobi Polynomial.  Polynomials obtained from the cycle index of symmetric groups were also shown to be equivalent to these orthogonal polynomials.  In this Chapter the parent sequence and its first convolution, the element sequence of even power polynomials are two sequences that are also expressed by the Jacobi and hypergeometric functions.

Board50 Integer Sequences and Orthogonal Polynomials