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- W3091775312 abstract "One of the first efforts towards the formation of the Calculus of Functions is due to Laplace, whose solution of the functional equation of the first order, by means of two equations in finite differences, is well known. Functional equations were afterwards treated systematically by Mr. Babbage; his memoirs were published in the Transactions of this Society, and there is some account of them in Professor Boole’s Treatise on the Calculus of Finite Differences. A very important functional equation was solved by Poisson in his Memoirs on Electricity; which suggested to me the investigations I have now the honour to lay before the Society. I have commenced by discussing the linear functional equation of the first order with constant coefficients, when the subjects of the unknown functions are rational functions of the independent variable, and have shown how the solution of such equations may in a variety of cases be effected by series, and by definite integrals. I have then considered functional equations with constant coefficients of the higher orders, and have proved that they may he solved by methods similar to those used for equations of the first order. I have next proceeded with the solution of functional equations with variable coefficients." @default.
- W3091775312 created "2020-10-15" @default.
- W3091775312 date "1862-12-31" @default.
- W3091775312 modified "2023-09-26" @default.
- W3091775312 title "XIV. On the calculus of functions" @default.
- W3091775312 doi "https://doi.org/10.1098/rstl.1862.0017" @default.
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