190 research outputs found
Recurrence relations for polynomial sequences via Riordan matrices
We give recurrence relations for any family of generalized Appell polynomials
unifying so some known recurrences of many classical sequences of polynomials.
Our main tool to get our goal is the Riordan group. We use the product of
Riordan matrices to interpret some relationships between different families of
polynomials. Moreover using the Hadamard product of series we get a general
recurrence relation for the polynomial sequences associated to the so called
generalized umbral calculus.Comment: 41 page
Combinatorial Aspects of the Generalized Euler's Totient
A generalized Euler's totient is defined as a Dirichlet convolution of a power function and a product of the Souriau-Hsu-Möbius function with a completely multiplicative function. Two combinatorial aspects of the generalized Euler's totient, namely, its connections to other totients and its relations with counting formulae, are investigated
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