HANKEL-TOTAL POSITIVITY OF SOME SEQUENCES.

The aim of this paper is to develop analytic techniques to deal with Hankel-total positivity of sequences. We show two nonlinear operators preserving Stieltjes moment property of sequences. They actually both extend a result of Wang and Zhu that if (an)n≥0 is a Stieltjes moment sequence, then so is (an+2an - a²n+1)n≥0. Using complete monotonicity of functions, we also prove Stieltjes moment properties of the sequences ...and .... Particularly in a new unified manner our results imply the Stieltjes moment properties of binomial coefficients (pn+r-1 n) and Fuss- Catalan numbers r/pn+r (pn+r n) proved by Mlotkowski, Penson, and Zyczkowski, and Liu and Pego, respectively, and also extend some results for log-convexity of sequences proved by Chen-Guo-Wang, Su-Wang, Yu, and Wang-Zhu, respectively. [ABSTRACT FROM AUTHOR]