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XXII.—New General Formulœ for the Transformation of Infinite Series into Continued Fractions

Published online by Cambridge University Press:  17 January 2013

Thomas Muir
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Extract

In Crelle's Journal, vol. x., Stern devotes fifteen pages (pp. 245-259) of his Theorie der Kettenbrüche to the examination and elucidation of the following problems:—

as continued fractions of the form

where a1, a2, a3, … are independent of x.

Type
Research Article
Information
Earth and Environmental Science Transactions of The Royal Society of Edinburgh , Volume 27 , Issue 4 , 1876 , pp. 467 - 471
Copyright
Copyright © Royal Society of Edinburgh 1876

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References

page 467 note * “ Hier scheint es vielmehr nothwendig zu sein, einen einfachen Ausdruck zu finden, welcher jeden Theilnenner am (oder jedes Nm, Nm+1) unmittelbar aus den Reihencoefficienten A1, A2, … finden lehrt. Der Verfasser hat sich vergebens bemüht die Lösung dieser Aufgabe zu finden, vielleicht aber können die mitgetheilten Ausdrücke für Nm, Nm+1, welche wohl nirgendwo angegeben sind, darauf führen.”—Crelle's Journal, vol. x. p. 257.

page 468 note * See paper on “Continuants” in the Proc. R. S. E. for 1873–74, and pamphlet on “ The Expression of a Quadratic Surd as a Continued Fraction,” Glasgow, 1874.

page 470 note † Disquisitio circa seriem infinitam in the Abhandl. der Götting. Gesellsch. d. Wissensch. Bd ii. 1812.

page 471 note * Opuscula Analytica, t. ii p. 138.

page 471 note † One such method has since been discovered by the author, and communicated to the Mathematical Society of London, in a paper read February 10th, 1876.