For m = 1,2,... and & integer, show that E(-1r () m 27) r=0
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The proof is by induction. The result is easily checked for m = 1,2, 3. Then assume and show that
First, prove for k < m + 1. For this purpose, use the identity
And in the process of the subsequent parts of the proof, use the expansion
Along with. In establishing for k = m + 1, write (m + 1 - 2r)m+l = (m + 1 - 2r)m (m + 1 - 2r), use the fact that
Repeatedly use the expansion just mentioned, and, of course, also employs relation.
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Related Book For
An Introduction to Measure Theoretic Probability
ISBN: 978-0128000427
2nd edition
Authors: George G. Roussas
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