Tirukkannapuram Vijayaraghavan

Tirukkannapuram Vijayaraghavan (Tamil: திருக்கண்ணபுரம் விஜயராகவன்; 30 November 1902 – 20 April 1955) was an Indian mathematician from the Madras region. He worked with G. H. Hardy when he went to Oxford in mid-1920s on Pisot–Vijayaraghavan numbers. He was a fellow of Indian Academy of Sciences elected in the year 1934. His father was a pandit.

Vijayaraghavan was well versed in Sanskrit and Tamil. He was a close friend of André Weil. Weil hired him in 1930 despite his lack of diploma, and they served together in Aligarh Muslim University.^[1] While Weil was away in Europe, Ross Masood planned to replace Weil's professorship with Vijayaraghavan, but Vijayaraghavan quit in protest and moved to the University of Dhaka.^[2]

Vijayaraghavan proved a special case of Herschfeld's theorem on nested radicals:^[3] For ${\displaystyle a_{n}>0}$

${\displaystyle {\sqrt {a_{1}+{\sqrt {a_{2}+{\sqrt {a_{3}+{\sqrt {a_{4}+\cdots }}}}}}}}}$

converges if and only if

${\displaystyle {\overline {\lim }}(\log a_{n})/2^{n}<+\infty ,}$

where ${\displaystyle {\overline {\lim }}}$ denotes the limit superior.