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10/13/2025

Using the Cauchy Product to establish a very useful generating function in the Theory of Harmonic Series.
09/25/2025

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.
07/07/2025

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 int...
07/07/2025

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.

07/07/2025

Another way to compute this Definite integral would be to split the interval at x = 1.
07/06/2025

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 th...
07/06/2025

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 Transfor...
07/05/2025

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

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