Generating functions for finite sums involving higher powers of binomial coefficients: Analysis of hypergeometric functions including new families of polynomials and numbers
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Mathematical Analysis and Applications"
DOI: 10.1016/j.jmaa.2019.05.015
Abstract: The origin of this study is based on not only explicit formulas of finite sums involving higher powers of binomial coefficients, but also explicit evaluations of generating functions for this sums. It should be emphasized… read more here.
Keywords: powers binomial; binomial coefficients; sums involving; new families ... See more keywords
Factors of sums involving q-binomial coefficients and powers of q-integers
Sign Up to like & getrecommendations! Published in 2017 at "Journal of Difference Equations and Applications"
DOI: 10.1080/10236198.2017.1355366
Abstract: Abstract We show that, for all positive integers , , and any non-negative integers j and r with , the expression is a Laurent polynomial in q with integer coefficients, where and . This gives… read more here.
Keywords: coefficients powers; sums involving; factors sums; involving binomial ... See more keywords
Estimates of shifted convolution sums involving Fourier coefficients of Hecke–Maass eigenform
Sign Up to like & getrecommendations! Published in 2021 at "International Journal of Number Theory"
DOI: 10.1142/s1793042121500524
Abstract: We obtain certain estimates for averages of shifted convolution sums involving the Fourier coefficients of a normalized Hecke–Maass eigenform and holomorphic cusp form. read more here.
Keywords: sums involving; fourier coefficients; involving fourier; hecke maass ... See more keywords
Binomial sums involving Catalan numbers
Sign Up to like & getrecommendations! Published in 2021 at "Rocky Mountain Journal of Mathematics"
DOI: 10.1216/rmj.2021.51.1221
Abstract: Recently, various interesting binomial sums involving Catalan numbers have been derived and computed. Inspired from them, several binomial sums involving Catalan numbers are evaluated in closed forms using a hypergeometric series approach. read more here.
Keywords: binomial sums; catalan numbers; involving catalan; sums involving ... See more keywords
The Power Sums Involving Fibonacci Polynomials and Their Applications
Sign Up to like & getrecommendations! Published in 2019 at "Symmetry"
DOI: 10.3390/sym11050635
Abstract: The Girard and Waring formula and mathematical induction are used to study a problem involving the sums of powers of Fibonacci polynomials in this paper, and we give it interesting divisible properties. As an application… read more here.
Keywords: fibonacci polynomials; polynomials applications; involving fibonacci; power sums ... See more keywords