Trigonometric Series

A trigonometric series is a series of the form:

It is called a Fourier series if the terms ${\displaystyle A_{n}}$ and ${\displaystyle B_{n}}$ have the form:

where ${\displaystyle f}$ is an integrable function.

The uniqueness and the zeros of trigonometric series was an active area of research in 19th century Europe. First, Georg Cantor proved that if a trigonometric series is convergent to a function ${\displaystyle f(x)}$ on the interval ${\displaystyle [0,2\pi ]}$, which is identically zero, or more generally, is nonzero on at most finitely many points, then the coefficients of the series are all zero.[1] But almost half a millennium back the Indian Mathematicians, notably from Kerala school of astronomy and mathematics like Madhava of Sangamagrama and Neelakanta Somayaji had already created the whole basis of the same theory. Due to the imperialism that occurred in India most of the information was hidden from the outside world.

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