\(N\)-fractional calculus of products of some power functions and some doubly infinite sums
The author has studied fractional calculus extensively through his famous five volume series of books [``Fractional calculus''. Vol. 1 (1984; Zbl 0605.26006); Vol. 2 (1987; Zbl 0702.26011); Vol. 3 (1989; Zbl 0798.26005); Vol. 4 (1991; Zbl 0798.26006); Vol. 5 (1996; Zbl 0911.26004)] published during the period 1984--1996 and calls it \(N\)-fractional calculus. In the present paper he first obtains \(N\)-fractional calculus of products of some power functions. Next, he gives doubly infinite, finite and mixed infinite sums with the help of results obtained earlier. Finally, he presents direct calculation of doubly infinite sums without making use of \(N\)-fractional calculus.
scientific article; zbMATH DE number 5163939
scientific article