Testwiki:Reference desk/Archives/Mathematics/2010 December 26

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December 26

Reference request for certain linear sequences of functions.

Hi all. I think I read somewhere in Wikipedia a name, and perhaps a reference, for sequences of functions satisfying a linear recurrence of the following form

$f_{k+1}(x)=a(x){f_k}^{\prime }(x)$

where each term is the derivative of the preceding one, times a fixed function $a(x)$. Does anybody have a clue? I'm not able to find it again.... --pma 09:37, 26 December 2010 (UTC)

Strangely Chapter 22 of Abramowitz-Stegun mentions no relations of this form of the notable sequences of orthogonal polynomials. – b_jonas 10:39, 26 December 2010 (UTC)