A connection between a generalized Pascal matrix and the hypergeometric function Original Research Article

The n × n generalized Pascal matrix P(t) whose elements are related to the hypergeometric function View the MathML source is presented and the Cholesky decomposition of P(t) is obtained. As a result, it is shown that View the MathML source is the solution of the Gaussʹs hypergeometric differential equation, x(1 − x)y″ + [1 + (a + b − 1)x]y′ − aby = 0 . where a and b are any nonnegative integers. Moreover, a recurrence relation for generating the elements of P(t) is given.