# Tirukkannapuram Vijayaraghavan

Tirukkannapuram Vijayaraghavan (Tamil: திருக்கண்ணபுரம் விஜயராகவன்; 30 November 1902 – 20 April 1955) was an Indian mathematician from 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, the only son of famous upanyasaka tirukkannapuram Pattappa Swamy. Pattappa Swamy, to this day, is considered to be one of the most important personalities in sri vaishnavam or ramanuja sampradayam in the 20th century. Vijayaraghavan was a close friend of André Weil. He served with him in Aligarh Muslim University. He later shifted to University of Dhaka, protesting Weil's firing from AMU.[1]

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

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

converges if and only if

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

## 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.