In this paper, we derive some new symmetric properties of 𝑘-Fibonacci numbers by making use of symmetrizing operator. We also give some new generating functions for the products of some special ...

Partition functions, which enumerate the distinct ways a positive integer may be expressed as a sum of positive integers, have long captivated mathematicians due to their deep connections with number ...

Trigonometric sums and summation formulas have long served as essential tools for elucidating periodic phenomena across mathematics and the physical sciences. These techniques entail the explicit ...