Relation To Power Series
The sequence an generated by a Dirichlet series generating function corresponding to:
where ΞΆ(s) is the Riemann zeta function, has the ordinary generating function:
Read more about this topic: Dirichlet Series
Famous quotes containing the words relation to, relation, power and/or series:
“A theory of the middle class: that it is not to be determined by its financial situation but rather by its relation to government. That is, one could shade down from an actual ruling or governing class to a class hopelessly out of relation to government, thinking of gov’t as beyond its control, of itself as wholly controlled by gov’t. Somewhere in between and in gradations is the group that has the sense that gov’t exists for it, and shapes its consciousness accordingly.”
—Lionel Trilling (1905–1975)
“There is a relation between the hours of our life and the centuries of time. As the air I breathe is drawn from the great repositories of nature, as the light on my book is yielded by a star a hundred millions of miles distant, as the poise of my body depends on the equilibrium of centrifugal and centripetal forces, so the hours should be instructed by the ages and the ages explained by the hours.”
—Ralph Waldo Emerson (1803–1882)
“But, with whatever exception, it is still true that tradition characterizes the preaching of this country; that it comes out of the memory, and not out of the soul; that it aims at what is usual, and not at what is necessary and eternal; that thus historical Christianity destroys the power of preaching, by withdrawing it from the exploration of the moral nature of man; where the sublime is, where are the resources of astonishment and power.”
—Ralph Waldo Emerson (1803–1882)
“Personality is an unbroken series of successful gestures.”
—F. Scott Fitzgerald (1896–1940)