Regularizations and finite ladders in multiple trigonometry

KUROKAWA, Nobushige; WAKAYAMA, Masato

J. Math. Soc. Japan, Tome 57 (2005) no. 4, p. 1197-1216 / Harvested from Project Euclid

Résumé

We provide an extended interpretation of the zeta regularized product in [D]. This allows us to get regularized product expressions of Hölder's double sine function and its companion, i.e. the double and triple trigonometric functions. The expressions may reasonably explain the ladder structure among these multiple trigonometric functions. We also introduce the notion of finite ladders of functions which helps us understand the meaning behind these regularizations.

Publié le : 2005-10-14
Classification: Riemann zeta function, multiple trigonometric function, zeta regularized product, Euler-Maclaurin formula, Weierstrass canonical form, 11M06, 11M36

@article{1150287310,
     author = {KUROKAWA, Nobushige and WAKAYAMA, Masato},
     title = {Regularizations and finite ladders in multiple trigonometry},
     journal = {J. Math. Soc. Japan},
     volume = {57},
     number = {4},
     year = {2005},
     pages = { 1197-1216},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1150287310}
}

KUROKAWA, Nobushige; WAKAYAMA, Masato. Regularizations and finite ladders in multiple trigonometry. J. Math. Soc. Japan, Tome 57 (2005) no. 4, pp.  1197-1216. http://gdmltest.u-ga.fr/item/1150287310/