| Abstrakt: |
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. [ABSTRACT FROM AUTHOR] |
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