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math.FA2021
A short study of generalized Dirichlet Integrals via tempered distributions
Cyril Belardinelli
In the present article, the author uses Fourier theory of tempered distributions (generalized functions) in deriving a formula for Dirichlet-like integrals. The applied method is r…
math.FA2021
A novel method of computing the volume of hyperspheres in finite and infinite dimensions
Cyril Belardinelli
In the present article, the volume of the hypersphere in n-dimensional euclidean space is recalculated in a rather original way by using the theory of generalized functions (temper…
math.FA2021
Fractional calculus of tempered distributions. A new approach
Cyril Belardinelli
In the present article, a new method for the evaluation of fractional derivatives of arbitrary real order is proposed. Numerous but inequivalent formulations have been given in the…