Generalizations to several variables of Lagrange's expansion, with applications to stochastic processes
- 24 October 1960
- journal article
- Published by Cambridge University Press (CUP) in Mathematical Proceedings of the Cambridge Philosophical Society
- Vol. 56 (4) , 367-380
- https://doi.org/10.1017/s0305004100034666
Abstract
A generalization to two independent variables of Lagrange's expansion of an inverse function was given by Stieltjes and proved rigorously by Poincaré. A new method of proof is given here that also provides a new and sometimes more convenient form of the generalization. The results are given for an arbitrary number of independent variables. Applications are pointed out to random branching processes, to queues with various types of customers, and to some enumeration problems.Keywords
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