On the Zeros of the Generating Functions of Multiply Positive Sequences and Functions
I. J. Schoenberg · Annals of Mathematics · 1955
has only real and negative zeros. A natural generalization of the concept of a totally positive sequence is as follows :2 Let k be a given natural integer. We say that the sequence I an } (an ? 0, Ean convergent) is k-times positive, or k-positive, provided the matrix (1.1) has no negative minor of order ? k. If we denote by (Pk the class of k-times positive sequences we have a shrinking sequence of classes