Chetuya Math Tutoring

Using the Cauchy Product to establish a very useful generating function in the Theory of Harmonic Series.

A very interesting Trigonometric sum with surprisingly beautiful closed form.

Here’s one way to simplify a definite integral with a complex denominator. From here we will try to investigate this integral for various values of an and see if a closed form structure is attainable.

Another way to compute this Definite integral would be to split the interval at x = 1.

Nothing like starting a day with a beautiful integral. Even more beautiful the closed form of this integral is simply the Catalan’s constant denoted by G.

The following beautiful integrals are consequences of this generalized Fresnel Integral established via Laplace Transform.