Logrithm - Generalizations - Related Concepts

Related Concepts

From the perspective of pure mathematics, the identity log(cd) = log(c) + log(d) expresses a group isomorphism between positive reals under multiplication and reals under addition. Logarithmic functions are the only continuous isomorphisms between these groups. By means of that isomorphism, the Haar measure (Lebesgue measure) dx on the reals corresponds to the Haar measure dx/x on the positive reals. In complex analysis and algebraic geometry, differential forms of the form df/f are known as forms with logarithmic poles.

The polylogarithm is the function defined by


operatorname{Li}_s(z) = sum_{k=1}^infty {z^k over k^s}.

It is related to the natural logarithm by Li1(z) = −ln(1 − z). Moreover, Lis(1) equals the Riemann zeta function ζ(s).

Read more about this topic:  Logrithm, Generalizations

Other articles related to "related concepts, related, concept":

Logogen Model - Related Concepts
... is the belief that the speed and accuracy with which a word is recognized is related to how frequently the word occurs in our language ... of acquisition – This term generally refers to the age at which a concept or skills is learned ...

Famous quotes containing the words concepts and/or related:

    During our twenties...we act toward the new adulthood the way sociologists tell us new waves of immigrants acted on becoming Americans: we adopt the host culture’s values in an exaggerated and rigid fashion until we can rethink them and make them our own. Our idea of what adults are and what we’re supposed to be is composed of outdated childhood concepts brought forward.
    Roger Gould (20th century)

    The question of place and climate is most closely related to the question of nutrition. Nobody is free to live everywhere; and whoever has to solve great problems that challenge all his strength actually has a very restricted choice in this matter. The influence of climate on our metabolism, its retardation, its acceleration, goes so far that a mistaken choice of place and climate can not only estrange a man from his task but can actually keep it from him: he never gets to see it.
    Friedrich Nietzsche (1844–1900)