Generalized q-integrals via neutrices: Application to the q-beta function | Zendy

Ahmed Salem | Zendy

AI Assistant Blog Pricing

Home ZAIA Blog

Open Access

Generalized q-integrals via neutrices: Application to the q-beta function

Author(s) -

Ahmed Salem

Publication year - 2013

Publication title -

filomat

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.449

H-Index - 34

eISSN - 2406-0933

pISSN - 0354-5180

DOI - 10.2298/fil1308473s

Subject(s) - mathematics , beta (programming language) , gamma function , function (biology) , incomplete gamma function , limit (mathematics) , beta function (physics) , pure mathematics , mathematical analysis , combinatorics , calculus (dental) , quantum mechanics , physics , evolutionary biology , quantum gravity , computer science , quantum , biology , programming language , relationship between string theory and quantum field theory , medicine , dentistry

Let f(x) be a continuous function defined on the interval (0,a). In this work, we apply the neutrix limit to generalize the q-integral ∫ a 0 x α−1 ln r xf(x)dqx, r ∈ N for all values of α ∈ R. We use our results to extend the definition of the q-beta function Bq(a,b) and its derivatives for all values of b and a , 0, −1, −2, · · ·. Some results for the q-gamma function are derived.

The content you want is available to Zendy users.

Already have an account? Click here to sign in.

Having issues? You can contact us here

Accelerating Research