Regularizations and finite ladders in multiple trigonometry

Nobushige KUROKAWA; Masato WAKAYAMA

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Regularizations and finite ladders in multiple trigonometry

机译：多重三角学中的正则化和有限阶梯

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摘要

We provide an extended interpretation of the zeta regularized product in [D]. This allows us to get regularized product expressions of Holder'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.

机译：我们在[D]中提供了zeta正则乘积的扩展解释。这使我们能够获得Holder的双正弦函数及其伴随函数的正则乘积表达式，即double和Triple三角函数。这些表达式可以合理地解释这些多个三角函数之间的阶梯结构。我们还介绍了函数有限阶梯的概念，这有助于我们理解这些正则化背后的含义。

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来源
《Journal of the Mathematical Society of Japan》 |2005年第4期|p.1197-1216|共20页
作者
Nobushige KUROKAWA; Masato WAKAYAMA;
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作者单位

Department of Mathematics Tokyo Institute of Technology Oh-okayama, Tokyo, 152-0033 Japan;

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收录信息美国《科学引文索引》(SCI);
原文格式 PDF
正文语种 eng
中图分类数学;
关键词
riemann zeta function; multiple trigonometric function; zeta regularized product; euler-maclaurin formula; weierstrass canonical form;

机译：riemann zeta函数;多个三角函数;zeta正则积;欧拉-麦克劳林公式;Weierstrass正则形式;

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7. Regularizations and finite ladders in multiple trigonometry [O] . Nobushige KUROKAWA, Masato WAKAYAMA 2005

机译：在多次三角学中的规程和有限梯子

Regularizations and finite ladders in multiple trigonometry

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