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XXXIV.—Summation of a Compound Series, and its Application to a Problem in Probabilities

Published online by Cambridge University Press:  17 January 2013

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Extract

The series propossed for solution in the follwing paper is—

The law of this series is manifest. Each term is the product of two factorials, the first consisting of p, and the latter of q factors. And in each successive term, the factors of the first factorial are each diminished by one, and those of the latter increased by one.

Type
Research Article
Information
Earth and Environmental Science Transactions of The Royal Society of Edinburgh , Volume 20 , Issue 4 , 1853 , pp. 541 - 545
Copyright
Copyright © Royal Society of Edinburgh 1853

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References

page 543 note * The coefficient (U of Galloway's Treatise), expressing the number of different ways in which p white and q black balls can be combined in p + q trials, is here omitted. This is immaterial, as it disappears in the expression .