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2214. Differential operators in Leibniz’s theorem and integration by parts

Published online by Cambridge University Press:  03 November 2016

C. Walmsley
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Type
Mathematical Notes
Information
The Mathematical Gazette , Volume 35 , Issue 312 , May 1951 , pp. 122 - 123
Copyright
Copyright © The Mathematical Association 1951

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References

* The notation used is that found in Phillips, A Course of Analysis. The proof is essentially the same as that given in Verblunsky, Functions of a Real Variable, p. 64, but the difference in notation brings out the analogy with the proof of the theorem on the permanence of the first differential. For similar proofs, see also Chaundy, , The Differential Calculus, p. 71 Google Scholar and Gibson, , Advanced Calculus, p. 66.Google Scholar

‡ Cf. Durell, and Robson, , Elementary Calculus, Vol. 1,Google Scholar Phillips, A Course of Analysis, and Stewart, Advanced Calculus, where it is pointed out that the proof using (3) only holds if this restriction is made.