Geodesic
Symmetric identity for polynomial sequences satisfying $A_{n+1}^\prime (x)=(n+1)A_n(x)$
Communications in Mathematics, Tome 29 (2021) no. 3, pp. 343-355

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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.
Classification : 05A19, 05A40, 11B68
Keywords: Appell sequence; Apostol-Bernoulli polynomial; Apostol-Euler polynomial; generalized Bernoulli polynomial; primitive Dirichlet character. 
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     title = {Symmetric identity for polynomial sequences satisfying $A_{n+1}^\prime (x)=(n+1)A_n(x)$},
     journal = {Communications in Mathematics},
     pages = {343--355},
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     zbl = {1480.05012},
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     url = {http://geodesic.mathdoc.fr/item/COMIM_2021__29_3_a1/}
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Bencherif, Farid; Boumahdi, Rachid; Garici, Tarek. Symmetric identity for polynomial sequences satisfying $A_{n+1}^\prime (x)=(n+1)A_n(x)$. Communications in Mathematics, Tome 29 (2021) no. 3, pp. 343-355. http://geodesic.mathdoc.fr/item/COMIM_2021__29_3_a1/