An application of theory of distributions to the family of λ-generalized gamma function

Abstract

Gamma function and its generalizations always have played a basic role in various disciplines. The aim of present study is to investigate a new representation of the λ-generalized gamma function. This representation is developed by using different modified forms of delta function. This development explores their extended use as generalized functions (distributions), which are meaningful to exist over some particular space of test functions. Further to this a discussion is presented for the suitable applications of this new representation.

Keywords

• λ-generalized gamma function
• fourier transformation
• slowly increasing test functions
• generalized functions (distributions)
• delta function