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Abstract
The main purpose of this paper is to construct generating functions for some families of Genocchi type polynomials. By applying the derivative operator to these generating functions, we define a function which interpolates these polynomials at negative integers. Among other results, we prove a multiplication theorem for these polynomials. Furthermore, we give several other identities and applications associated with these and related polynomials and their interpolation functions.
Keywords:
- generating functions
- Genocchi numbers
- Genocchi polynomials
- Euler numbers
- Euler polynomials
- Bernoulli numbers
- Bernoulli polynomials
- Apostol type polynomials
- Taylor–Maclaurin series expansions
- interpolation functions
- sums of powers of natural numbers
- multinomial coefficients
- Riemann zeta function
- Hurwitz (or generalized) zeta functions
- Hurwitz–Lerch zeta function
2010 Mathematics Subject Classifications :
Acknowledgements
The present investigation was supported by the Scientific Research Fund of the Project Administration of the University of Akdeniz.