Formulas for Some Restricted Partition Functions - Songvilay, Sonexay; Saybounheaung, Thongsouk; Namkhaluck, Innavanh; Thanavanh, Pinkham; Viengthany, Kaisone (Souphanouvong University Journal Multidisciplinary Research and Development, 2021)
The purposes of this research are to find formulas for some restricted partition functions valid for all positive integers and for some finite subset of the natural numbers. In particular, the method of Andrews and Eriksson is modified for some conditions of elements in the set where and using the generating function, partial fraction expansion, partial fractions, the greatest integer function and the nearest integer function. The results of this research found that finding formulas for some partition functions can be discovered as the set of prime numbers from to and the set of even numbers from to