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2017, vol. 41, br. 1, str. 121141

Explicit and recursive formulas, integral representations, and properties of the large Schröder numbers
(naslov ne postoji na srpskom)
^{a}Institute of Mathematics, Henan Polytechnic University, Jiaozuo City, Henan Province, China + College of Mathematics, Inner Mongolia University for Nationalities, Tongliao City, Inner Mongolia Autonomous Region, China + Department of Mathematics, College of Science, Tianjin Polytechnic University, Tianjin City, China ^{b}School of Mathematics and Informatics, Henan Polytechnic University, Jiaozuo City, Henan Province, China
eadresa: qifeng618@gmail.com, bai.ni.guo@hotmail.com
Ključne reči: large Schroder number; little Schroder number; generating function; explicit formula; recursive formula; integral representation; convexity; logarithmic convexity; complete monotonicity; determinantal inequality; product inequality; central Delannoy numbers; rel
Sažetak
(ne postoji na srpskom)
In the paper, the authors review and survey some new results on the large Schroder numbers. These results were obtained by the authors and their coauthors from January 2016 and can be summarized up as follows. (a) By studying the generating function of the large Schroder numbers, the authors and their coauthors establish several explicit formulas and a recursive formula for the large Schroder numbers and present relations between the Schroder numbers and central Delannoy numbers. (b) By utilizing the Cauchy integral formula in the theory of complex functions, the authors and their coauthors build several integral representations for the large Schroder numbers and their generating function. (c) By employing integral representations for the large Schroder numbers, the authors and their coauthors find some properties, including the convexity, complete monotonicity, product inequalities, and determinantal inequalities, of the large Schroder numbers.



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