Fractional Bernoulli Numbers And Polynomials

In this thesis, we investigate the fractional Bernoulli numbers Ba;m and poly-rnnomials Ba;m(z) for all positive fractions a = rn ; 6= 0. We establish severalrnproperties of these numbers and polynomials which are analogous to the clas-rnsical as well as hypergeometric Bernoulli numbers and polynomials. We alsorndevelop the higher order fractional Bernoulli numbers B(t)rna;m and polynomialsrnB(t)rna;m(z) and their connection to other identity.

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