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The set of L^p-functions (where p>=1) generalizes L2-space. Instead of square integrable, the measurable function f must be p-integrable for f to be in L^p. On a measure ...

Physicists and engineers use the phrase "order of magnitude" to refer to the smallest power of ten needed to represent a quantity. Two quantities A and B which are within ...

If (1-z)^(alpha+beta-gamma-1/2)_2F_1(2alpha,2beta;2gamma;z)=sum_(n=0)^inftya_nz^n, (1) where _2F_1(a,b;c;z) is a hypergeometric function, then (2) where (a)_n is a Pochhammer ...

_2F_1(a,b;c;1)=((c-b)_(-a))/((c)_(-a))=(Gamma(c)Gamma(c-a-b))/(Gamma(c-a)Gamma(c-b)) for R[c-a-b]>0, where _2F_1(a,b;c;x) is a (Gauss) hypergeometric function. If a is a ...

Let f(x,y)=u(x,y)+iv(x,y), (1) where z=x+iy, (2) so dz=dx+idy. (3) The total derivative of f with respect to z is then (df)/(dz) = ...

The duplication formula for Rogers L-function follows from Abel's functional equation and is given by 1/2L(x^2)=L(x)-L(x/(1+x)).

A convex body in Euclidean space that is centrally symmetric with center at the origin is determined among all such bodies by its brightness function (the volume of each ...

A mathematical object (such as a set or function) is said to bounded if it possesses a bound, i.e., a value which all members of the set, functions, etc., are less than.

If a and n are relatively prime so that the greatest common divisor GCD(a,n)=1, then a^(lambda(n))=1 (mod n), where lambda is the Carmichael function.

An expansion based on the roots of x^(-n)[xJ_n^'(x)+HJ_n(x)]=0, where J_n(x) is a Bessel function of the first kind, is called a Dini expansion.