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XIII.—Continuants resolvable into Linear Factors

Published online by Cambridge University Press:  06 July 2012

Thomas Muir
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Extract

(1) It is known that a continuant whose three diagonals are formed of certain equidifferent progressions is resolvable into linear factors, the earliest specimens placed on record being those of Sylvester and Painvin. The object of the present paper is to show that there are continuants of quite a different type which are also so resolvable, and to expound a general mode of investigating the subject.

Type
Research Article
Information
Earth and Environmental Science Transactions of The Royal Society of Edinburgh , Volume 41 , Issue 2 , 1906 , pp. 343 - 358
Copyright
Copyright © Royal Society of Edinburgh 1906

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References

page 343 note * [Sylvester, J. J.] “Théorème sur les déterminants de M. Sylvester,” Nour. Annales de Math., xiii. p. 305.

Painvin, “Sur un certain système d'équations linéaires,” Journ. de Liourille, 2e sér., iii. pp. 41-46.

Muir, Thomas. “Factorizable Continuants,” Trans. S. Afr. Philos. Soc., xiv. pp. 29-33.