# A new identity relating a polynomial to infinite series of the hyperbolic secant functions

## Document Type

Article

## Publication Date

11-30-2021

## Abstract

Hyperbolic functions do not form a complete set and in general it is not possible to expand a given function as an infinite series of hyperbolic functions. Here, we take the classical problem of steady laminar flow in a rectangular duct and turn the duct 90°. The maximum velocity in the duct should remain unchanged if the flow is driven by the same pressure gradient. This leads to a new identity that relates a second-order polynomial to infinite series of the hyperbolic secant functions. We discuss the mathematical properties of this identity and verify it by two different methods.

## Publication Source (Journal or Book title)

Academia Letters

## Recommended Citation

Wong, H.
(2021). A new identity relating a polynomial to infinite series of the hyperbolic secant functions.* Academia Letters*
Retrieved from https://repository.lsu.edu/mechanical_engineering_pubs/426