Generating functions for multiple zeta star values
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Journal de Théorie des Nombres de Bordeaux, Volume 31 (2019) no. 2, pp. 343-360.

We study generating functions for multiple zeta star values in general form. These generating functions provide a connection between multiple zeta star values and multiple Euler sums, which allows us to express each multiple zeta star value in terms of multiple alternating Euler sums, and specifically, reduce the length of blocks of twos in the resulting sums.

Nous étudions les fonctions génératrices des valeurs des fonctions polyzêta ζ * (s 1 ,...,s m ) dans le cadre général. Ces fonctions génératrices établissent un lien entre les nombres polyzêta et les sommes d’Euler multiples, ce qui nous permet d’exprimer chaque valeur polyzêta en termes de sommes d’Euler multiples alternées, et notamment réduire la longueur des blocs de deux dans les sommes résultantes.

Received : 2018-09-09
Accepted : 2019-05-11
Published online : 2019-10-29
DOI : https://doi.org/10.5802/jtnb.1084
Classification:  11M32,  11M35,  05A15,  30B10,  30D05,  39B32
Keywords: Multiple zeta star value, multiple zeta value, generating function, Euler sum
@article{JTNB_2019__31_2_343_0,
     author = {Khodabakhsh Hessami Pilehrood and Tatiana Hessami Pilehrood},
     title = {Generating functions for multiple zeta star values},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
     publisher = {Soci\'et\'e Arithm\'etique de Bordeaux},
     volume = {31},
     number = {2},
     year = {2019},
     pages = {343-360},
     doi = {10.5802/jtnb.1084},
     language = {en},
     url={jtnb.centre-mersenne.org/item/JTNB_2019__31_2_343_0/}
}
Hessami Pilehrood, Khodabakhsh; Hessami Pilehrood, Tatiana. Generating functions for multiple zeta star values. Journal de Théorie des Nombres de Bordeaux, Volume 31 (2019) no. 2, pp. 343-360. doi : 10.5802/jtnb.1084. https://jtnb.centre-mersenne.org/item/JTNB_2019__31_2_343_0/

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