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In the paper, with the aid of the Fa\`a di Bruno formula, in terms of centralfactorial numbers of the second kind, and with the terminology of the Stirlingnumbers of the second kind, the authors derive several series expansions forany positive integer powers of the sinc and sinhc functions, discover severalclosed-form formulas for partial Bell polynomials of all derivatives of thesinc function, establish several series expansions for any real powers of thesinc and sinhc functions, and present several identities for central factorialnumbers of the second kind and for the Stirling numbers of the second kind.

applicable analysis and discrete mathematics

Several series expansions for real powers and several formulas for  partial Bell polynomials of sinc and sinhc functions in terms of central  factorial and Stirling numbers of second kind