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On the Peano Derivatives

Published online by Cambridge University Press:  20 November 2018

P. S. Bullen  and
S. N. Mukhopadhyay
P. S. Bullen
Affiliation:
University of British Columbia, Vancouver, British Columbia
S. N. Mukhopadhyay
Affiliation:
University of British Columbia, Vancouver, British Columbia
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Let f be a real valued function defined in some neighbourhood of a point x. If there are numbers α 1, α 2, … α r-1, independent of h such that

then the number αk is called the kth Peano derivative (also called kth de la Vallée Poussin derivative [6]) of f at x and we write αk = fk(x). It is convenient to write α 0 = f 0(x) = f(x). The definition is such that if the mth Peano derivative exists so does the nth for 0 ≦ n ≦ m.

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 25 , Issue 1 , February 1973 , pp. 127 - 140
Copyright
Copyright © Canadian Mathematical Society 1973

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