View source for Symmetric difference of order n

''at a point <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/s/s091/s091630/s0916302.png" /> of a function <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/s/s091/s091630/s0916303.png" /> of a real variable''

The expression

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The following expression is often also referred to as a symmetric difference:

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It is obtained from the above by substituting <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/s/s091/s091630/s0916306.png" /> for <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/s/s091/s091630/s0916307.png" />. If <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/s/s091/s091630/s0916308.png" /> has an <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/s/s091/s091630/s0916309.png" />-th order derivative <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/s/s091/s091630/s09163010.png" /> at <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/s/s091/s091630/s09163011.png" />, then

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====References====
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  H. Meschkowski,   "Differenzengleichungen" , Vandenhoeck &amp; Ruprecht  (1959)</TD></TR><TR><TD valign="top">[a2]</TD> <TD valign="top">  L.N. Milne-Thomson,   "The calculus of finite differences" , Chelsea, reprint  (1981)</TD></TR><TR><TD valign="top">[a3]</TD> <TD valign="top">  N.E. Nörlund,   "Volesungen über Differenzenrechnung" , Chelsea, reprint  (1954)</TD></TR></table>