Publicação: Fractional Calculus of the Lerch Zeta Function
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This paper deals with the fractional derivative of the Lerch zeta function. We compute the fractional derivative of the Lerch zeta function using a complex generalization of the Grünwald–Letnikov derivative. This definition of fractional derivative, fulfilling the generalized Leibniz rule, allows us to derive a functional equation for the fractional derivative of the Lerch zeta function. This functional equation is rewritten in a simplified form that reduces its computational cost. Furthermore, we prove an approximate functional equation for the fractional derivative of the Lerch zeta function.
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computational cost, functional equation, generalized Leibniz rule, Grünwald–Letnikov fractional derivative, Lerch zeta function
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Inglês
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Mediterranean Journal of Mathematics, v. 19, n. 3, 2022.
