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Krishnamachari, C.
- On a General Theorem Relating to the Product of Two Determinants
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The Journal of the Indian Mathematical Society, Vol 15 (1924), Pagination: 73-90Abstract
[We have contributed in a series of papers our researches relating to the evaluation of certain classes of determinants to the Journal of the Indian Mathematical Society. The main results relating to persymmetrics have been communicated to the London Mathematical Society. In the course of our work, we have discovered a very elegant theorem, which has many interesting applications. In particular, we find that most of the results proved in our previous papers can be deduced from this theorem. This paper contains this theorem and some of its applications].
- On the Co-Efficients in the Expansion of cn (x,k)
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The Journal of the Indian Mathematical Society, Vol 15 (1924), Pagination: 98-99Abstract
Hancock in his Theory of Elliptic Functions, Vol. I, page 252, gives the first five co-efficients in the expansion of cn (x,k), as having been calculated by Gudermann in Crelle, Bd. XIX, p. 80. The authors pointed out in their paper : "Determinants involving Specified Numbers," Vol. XIV, No. 4, J. I. M. S., pp. 122-138, that the ascending Σ-table formed with a2n-1 = (2n-1)2, a2n = (2n)2k2 gives the co-efficients in the expansion of cn(x,k) and that with a2n-1 = (2n-1)2k2, a2n = (2n)2 gives the co-efficients in the expansion of dn (x,k)-Ibid, pp. 133, § 6.- The Operator (x, L)n
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