# Tirukkannapuram Vijayaraghavan

Thirukannapuram Vijayaraghavan
Born 30 November 1902
Died April 20, 1955 (aged 52)
Occupation mathematician

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.

Vijayaraghavan was well versed in Sanskrit and Tamil. He was a close friend of André Weil. He served with him in Aligarh Muslim University. He later moved to University of Dhaka, to protest at Weil's firing from AMU.[1]

Vijayaraghavan proved a special case of Herschfeld's theorem on nested radicals:[2] 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.

## References

1. ^
2. ^ Ramanujan, S. Collected Papers of Srinivasa Ramanujan (Ed. G. H. Hardy, P. V. S. Aiyar, and B. M. Wilson). Providence, RI: American Mathematical Society (2000), p. 348.