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The term energy has an important physical meaning in physics and is an extremely useful concept. There are several forms energy defined in mathematics. In measure theory, let ...

The function defined by chi_nu(z)=sum_(k=0)^infty(z^(2k+1))/((2k+1)^nu). (1) It is related to the polylogarithm by chi_nu(z) = 1/2[Li_nu(z)-Li_nu(-z)] (2) = ...

For any algebraic number x of degree n>2, a rational approximation p/q to x must satisfy |x-p/q|>1/(q^n) for sufficiently large q. Writing r=n leads to the definition of the ...

The Mercator series, also called the Newton-Mercator series (Havil 2003, p. 33), is the Taylor series for the natural logarithm ln(1+x) = sum_(k=1)^(infty)((-1)^(k+1))/kx^k ...

For any M, there exists a t^' such that the sequence n^2+t^', where n=1, 2, ... contains at least M primes.

Let P(E_i) be the probability that E_i is true, and P( union _(i=1)^nE_i) be the probability that at least one of E_1, E_2, ..., E_n is true. Then "the" Bonferroni ...

The modulus of a complex number z, also called the complex norm, is denoted |z| and defined by |x+iy|=sqrt(x^2+y^2). (1) If z is expressed as a complex exponential (i.e., a ...

A global field is either a number field, a function field on an algebraic curve, or an extension of transcendence degree one over a finite field. From a modern point of view, ...

The study of number fields by embedding them in a local field is called local class field theory. Information about an equation in a local field may give information about ...

A field which is complete with respect to a discrete valuation is called a local field if its field of residue classes is finite. The Hasse principle is one of the chief ...