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