A Proof Of New Summation Formulas By Using Sampling Theorems
Abbreviated Journal Title
Proc. Amer. Math. Soc.
TRIGONOMETRIC SERIES; BESSEL FUNCTIONS; HYPERGEOMETRIC FUNCTIONS; SHANNON AND KRAMER SAMPLING THEOREMS; STURM-LIOUVILLE PROBLEMS; LAGRANGE INTERPOLATION; Mathematics, Applied; Mathematics
Using symbolic manipulation programs, William Gosper has obtained in the last two years new, but unusual, summation formulae involving trigonometric functions. Recently, Ismail and Zhang have been able to prove mathematically some of these formulae and generalize them to summation formulae involving the Bessel functions of the first kind. In this paper we show that some of Gosper's formulae, as well as their generalization by Ismail and Zhang, can be obtained from already known results in sampling theory. Moreover, we show that sampling theory can actually produce other new summation formulae, involving different kinds of special functions, in a straightforward fashion.
Proceedings of the American Mathematical Society
"A Proof Of New Summation Formulas By Using Sampling Theorems" (1993). Faculty Bibliography 1990s. 968.