Scientific Serials

    Article metrics


    American Journal of Mathematics, vol. xxi. No. 2, April.—On systems of multiform functions belonging to a group of linear substitutions with uniform coefficients, by E. J. Wilczynski. In this memoir, the author attempts to prove the existence of certain general functions, studied herein, he believes, for the first time. The existence of a large and important class of these functions is demonstrated by an indirect method, which con sists essentially in generalising the hypergeometric functions in a proper manner. The work is connected in a way with the researches of Fuchs, Schwarz and Neumann (on Riemann's theory of Abelian functions, and of Klein (Math. Ann., Bd. 41). Oskar Bolza states that his principal object, in his paper on the partial differential equations for the hyperelliptic θ and σ functions, is to replace part of Wiltheiss's work (Crelle, Bd. 99, and Math. Ann., Bd., 29, 31 and 33) by simpler and more direct proofs.—E. B. Van Vleck contributes an article on certain differential equations of the second order allied to Hermite's equation. The treatment is thorough, and the work is accompanied with numerous diagrams.

    Rights and permissions

    Reprints and Permissions

    About this article

    Cite this article

    Scientific Serials. Nature 60, 90 (1899) doi:10.1038/060090b0

    Download citation


    By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.