[Book Reviews]


    THE book under notice constitutes a valuable addition to the scanty literature of the calculus of functions, so called by de Morgan. Chap. i. deals with the functional equations forming the basis of proofs of the parallelogram of forces, with extensions to non-Euclidean statics, trigonometry and geometry. Chap. ii. treats of the functional equations expressing rational addition and multi plication theorems of uniform functions, with applications to elliptic functions and to Poincaré's transcendents. Chap. iii. deals with the canon ical difference equation of the first order, with applications to doubly periodic functions of the first and second kinds and to Picard's transcend ents. The last chapter brings a discussion of the functional equations of Abel and of Schröder, and concludes with an application of Fredholm's equation to the problem of Dirichlet for the po tential of C. Neumann. As might be expected from such a master of his craft, M. Picard has treated a variety of difficult problems in a most elegant and stimulating manner, thus demon strating the great power of methods based on functional equations, and his book can be highly recommended to all interested in this subject.

    Leçons sur quelques équations fonctionnelles avec des applications à divers problèmes d'analyse et de physique mathématique.

    Par Prof. Émile Picard. Rédigées par Eugène Blanc. (Cahiers scientifiques, publiés sous la direction de Gaston Julia, Fascicule 3.) Pp. v + 187. (Paris: Gauthier-Villars et Cie, 1928.) 40 francs.

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    [Book Reviews]. Nature 123, 126 (1929). https://doi.org/10.1038/123126b0

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