Asymptotic formulas for stacks and unimodal sequences

Asymptotic formulas for stacks and unimodal sequences

We study enumeration functions for unimodal sequences of positive integers, where the size of a sequence is the sum of its terms. We survey known results for a number of natural variants of unimodal sequences, including Auluck’s generalized Ferrers diagrams, Wright’s stacks, and Andrews’ convex compositions. These results describe combinatorial properties, generating functions, and asymptotic f...

Unimodal inversion sequences and related pattern classes

Four of these classes were separately shown previously to be enumerated by this sequence, while the five others are new. In chronological order of publication, see [1, Lemma 10] for T2, [4, Example 6.4] for T9, [9, Theorems 3.4 and 3.5] for T4, and [3, Section 3.3] for T8. The same sequence also enumerates unimodal inversion sequences [8]. An inversion sequence (subexcedant sequence, a reversal...

Some Asymptotic Formulas for Multiplicative Functions

Asymptotic Formulas for Generalized Elliptic-type Integrals

Epstein-Hubbell [6] elliptic-type integrals occur in radiation field problems. The object of the present paper is to consider a unified form of different elliptic-type integrals, defined and developed recently by several authors. We obtain asymptotic formulas for the generalized elliptic-type integrals. Keywords—Elliptic-type Integrals, Hypergeometric Functions, Asymptotic Formulas.

Some Asymptotic Formulas for Wiener Integralso