Abstract
ITNTEGRAL equations are not a quite modern invention, because a particular example was solved by Abel so far back as 1826. But an immense impetus was given to the subject by the papers of Volterra and Fredholm, especially by those of the latter; and the reason is not difficult to find. In the first place, Fredholm chose a standard form of equation obviously suited for a process of continued approximation; and what is much more important, a happy induction led him to the discovery that the solution could be put into the form of the quotient of one integral function of the parameter (λ) by another integral function. In a certain way this is analogous to Jacobi' s expression of his elliptic functions as ratios of theta-functions; and the simplicity and elegance of the formulae are due to a similar cause.
Introduction à la Théorie des Équations Intégrales.
By Prof. T. Lalesco. Pp. vii + 152. (Paris: A. Hermann et Fils, 1912.) Price 4 francs.
L'Équation de Fredholm et ses applications à la Physique Mathématique.
By Prof. H. B. Heywood Prof. M. Fréchet. Pp. vi + 165.(Paris: A. Hermann et Fils, 1912.) Price 5 francs.
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M., G. Introduction à la Théorie des Équations Intégrales L'Équation de Fredholm et ses applications à la Physique Mathématique . Nature 89, 499–500 (1912). https://doi.org/10.1038/089499a0
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DOI: https://doi.org/10.1038/089499a0
