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Keywords:
Appell sequence; Apostol-Bernoulli polynomial; Apostol-Euler polynomial; generalized Bernoulli polynomial; primitive Dirichlet character.
Appell sequence; Apostol-Bernoulli polynomial; Apostol-Euler polynomial; generalized Bernoulli polynomial; primitive Dirichlet character.
Summary:
Using umbral calculus, we establish a symmetric identity for any sequence of polynomials satisfying $A_{n+1}^\prime (x) =(n+1)A_{n}(x)$ with $A_0(x)$ a constant polynomial. This identity allows us to obtain in a simple way some known relations involving Apostol-Bernoulli polynomials, Apostol\HH Euler polynomials and generalized Bernoulli polynomials attached to a primitive Dirichlet character.
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