1. On fractional Stieltjes constants.
- Author
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Farr, Ricky E., Pauli, Sebastian, and Saidak, Filip
- Abstract
Abstract We study the non-integral generalized Stieltjes constants γ α (a) arising from the Laurent series expansions of fractional derivatives of the Hurwitz zeta functions ζ (α) (s , a) , and we prove that if h a (s) ≔ ζ (s , a) − 1 ∕ (s − 1) − 1 ∕ a s and C α (a) ≔ γ α (a) − log α (a) a , then C α (a) = (− 1) − α h a (α) (1) , for all real α ≥ 0 , where h (α) (x) denotes the α -th Grünwald–Letnikov fractional derivative of the function h at x. This result confirms the conjecture of Kreminski (2003), originally stated in terms of the Weyl fractional derivatives. [ABSTRACT FROM AUTHOR]
- Published
- 2018
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