Towards Problem Solving – Abhirup Moitra Blogs

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Abhirup Moitra

Unpacking Laurent Expansions in Complex Analysis

In complex analysis, one of the most powerful tools for understanding functions near singularities is the Laurent series. While the Taylor series expresses a function as an…

Mathematical Induction-II

“Eliminate all other factors, and the one which remains must be the truth.” ~Sherlock Holmes (The Sign of Four)

Madhava–Leibniz Series

"It has long been an axiom of mine that the little things are infinitely the most important." ~Sherlock Holmes (A Case of Identity)

Mathematical Induction-I

It is a capital mistake to theorize before you have all the evidence. It biases the judgment. ~ Sherlock Holmes (A Study in Scarlet)

Basel Problem:Using Resolution Into Factors

Leonard Euler’s calculational prowess was remarkable, including his work in the area of infinite series. His methods are not covered in this article, but we will state and…

Integration by Reduction Formulae

A reduction formula is often used in integration for working out integrals of higher order. It is lengthy and tedious to work across higher-degree expressions, and here the…

Integration of Inverse Functions

God does not care about our mathematical difficulties. He integrates empirically.— Albert Einstein

An Exceptional Relationship between two Transcedental

The mathematical and rigorous proof of this fact is that which is bigger \(e^{\pi}\) or \({\pi}^e\) is quite abstract. In this case, the mathematical arguments will not…