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Congruence Properties of G-Functions

Published online by Cambridge University Press:  20 January 2009

Hansraj Gupta
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Denoting the sum of the products of the first n natural numbers taken r at a time by the symbol G(n, r), I have shown that

with the initial values and

In general it was shown that

Defining G (x, r) by the fundamental relation:

for all values of x, we get

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 4 , Issue 2 , January 1935 , pp. 61 - 66
Copyright
Copyright © Edinburgh Mathematical Society 1935

References

page 61 note 1 “Sums of Products of first n natural numbers taken r at a time.” Journal of the Indian Math. Society, Vol. XIX, Part II, pp. 1–6.Google Scholar

page 65 note 1 Lemma 1 in my paper on “"A Theorem of Gauss,” to be published in the next number of these Proceedings.