The collected mathematical papers of arthur cayley, scd, frs
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ABSTRACT THIS instalment of the papers illustrates in a remarkable way Cayley's power of commenting upon and developing the work of his predecessors. The various memoirs on single and
double theta-functions are, of course, based upon the results of Rosenhain, Göpel, and Kummer; and it is instructive to see how Cayley's instinct for symmetry and logical consistency
has enabled him to present the theory in a compact and intelligible form. In the case of the single theta-functions, defined by their expansions in series, we have equations such as and from
these it appears that any three of the squared functions θ2_gh_(_u_) are connected by a linear relation. Hence we may take the squared functions to be proportional to A(_a-x_), B(_b-x_),
(_c-x_), D(_d-x_) with _x_ a variable, and the other quantities constant. Finally it is shown that _x_ and _u_ are connected by a differential equation of the form The Collected Mathematical
Papers of Arthur Cayley, Sc.D., F.R.S. Vols. x., xi. Pp. xiv + 616; xvi + 644. (Cambridge: at the University Press, 1896.) Access through your institution Buy or subscribe This is a preview
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_Nature_ 58, 50 (1898). https://doi.org/10.1038/058050a0 Download citation * Issue Date: 19 May 1898 * DOI: https://doi.org/10.1038/058050a0 SHARE THIS ARTICLE Anyone you share the following
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