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Friday, June 28

A Surprising Connection Between Green’s Functions and the
Infinite Product Representation of Elementary Functions

Yuri Melnikov, Middle Tennessee State University, Murfreesboro
Computer Science and Mathematics Division Seminar
2:00 PM — 3:00 PM, Joint Institute for Computational Sciences (Building 5100), Auditorium (Room 128)
Contact: Clayton Webster (, 865.574.3649


Some standard as well as innovative approaches will be reviewed for the construction of Green's functions for the elliptic PDEs. Based on that, a surprising technique is proposed for obtaining infinite product representations of some trigonometric, hyperbolic, and special functions. The technique uses comparison of different alternative expressions of Green's functions constructed by different methods. This allows us not only obtain the classical Euler's formulas but also come up with a number of new representations.