A new regularization scheme for divergent power sums sum n^alpha uses fractional extensions of differential generators applied to a generalized spectral function, recovering zeta regularization under a consistency condition for continuous extension from integers.
Finite-part integration of the Hilbert trans- form
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Regularization of Divergent Power Sums via Fractional Extension of Differential Generators
A new regularization scheme for divergent power sums sum n^alpha uses fractional extensions of differential generators applied to a generalized spectral function, recovering zeta regularization under a consistency condition for continuous extension from integers.