ON THE q-EXTENSIONS OF THE BERNOULLI AND EULER NUMBERS, RELATED IDENTITIES AND LERCH ZETA FUNCTION
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Recently, λ-Bernoulli and λ-Euler numbers are studied in [5, 10]. The purpose of this paper is to present a systematic study of some families of the q-extensions of the λ-Bernoulli and λ-Euler numbers using the bosonic p-adic q-integral and the fermionic p-adic q-integral. The study of these λ-q-Bernoulli and λ-q-Euler numbers leads to interesting identities related to these objects. The results of the present paper cover earlier results concerning the q-Bernoulli and q-Euler numbers. We give the q-extensions of Lerch zeta function using the derivative operator to the generating functions of the λ-q-Bernoulli and λ-q-Euler numbers.
Abstract
Recently, λ-Bernoulli and λ-Euler numbers are studied in [5, 10]. The purpose of this paper is to present a systematic study of some families of the q-extensions of the λ-Bernoulli and λ-Euler numbers using the bosonic p-adic q-integral and the fermionic p-adic q-integral. The study of these λ-q-Bernoulli and λ-q-Euler numbers leads to interesting identities related to these objects. The results of the present paper cover earlier results concerning the q-Bernoulli and q-Euler numbers. We give the q-extensions of Lerch zeta function using the derivative operator to the generating functions of the λ-q-Bernoulli and λ-q-Euler numbers.
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