Laplace, Legendre, and Gauss

Part of the Studies in the History of Mathematics and Physical Sciences book series (HISTORY, volume 2)


Laplace’s efforts in our field appear both in his work on celestial mechanics and on probability theory. Moreover these contributions, which overlap each other and those of Gauss very much, are central to the interests of Laplace. One of his chief tools was that of the generating function. He was perhaps the first to exploit fully the generating function of a sequence y0, y1, y2,... . He wrote the function as
$$u={{y}_{0}}+{{y}_{1}}t+{{y}_{2}}{{t}^{2}}+{{y}_{3}}{{t}^{3}}+...+{{y}_{x}}{{t}^{x}}+{{y}_{x+1}}{{t}^{x+1}}+...+{{y}^{\infty }}{{t}_{\infty }}$$
without any consideration of convergence. Let us accept his formalistic approach and see how the generating function tool, which he used so powerfully, could produce various interpolation formulas.1


Linear Partial Difference Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag, New York, Inc. 1977

Authors and Affiliations

  1. 1.IBM ResearchNew YorkUSA
  2. 2.Institute for Advanced StudyPrincetonUSA

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