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The ordinary differential equation y^('')+r/zy^'=(Az^m+s/(z^2))y. (1) It has solution y=c_1I_(-nu)((2sqrt(A)z^(m/2+1))/(m+2))z^((1-r)/2) ...

It is possible to construct simple functions which produce growing patterns. For example, the Baxter-Hickerson function f(n)=1/3(2·10^(5n)-10^(4n)+2·10^(3n)+10^(2n)+10^n+1) ...

In accounting, the principal is the original amount borrowed or lent on which interest is then paid or given. The word "principal" is also used in many areas of mathematics ...

A fractional integral of order 1/2. The semi-integral of t^lambda is given by D^(-1/2)t^lambda=(t^(lambda+1/2)Gamma(lambda+1))/(Gamma(lambda+3/2)), so the semi-integral of ...

A fractional derivative of order 1/2. The semiderivative of t^lambda is given by D^(1/2)t^lambda=(t^(lambda-1/2)Gamma(lambda+1))/(Gamma(lambda+1/2)), so the semiderivative of ...

A seminorm is a function on a vector space V, denoted ||v||, such that the following conditions hold for all v and w in V, and any scalar c. 1. ||v||>=0, 2. ||cv||=|c|||v||, ...

The Legendre symbol is a number theoretic function (a/p) which is defined to be equal to +/-1 depending on whether a is a quadratic residue modulo p. The definition is ...

Lehmer's totient problem asks if there exist any composite numbers n such that phi(n)|(n-1), where phi(n) is the totient function? No such numbers are known. However, any ...

Newton's method for finding roots of a complex polynomial f entails iterating the function z-[f(z)/f^'(z)], which can be viewed as applying the Euler backward method with ...

In general, a singularity is a point at which an equation, surface, etc., blows up or becomes degenerate. Singularities are often also called singular points. Singularities ...