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The definite integral int_a^bx^ndx={(b^(n+1)-a^(n+1))/(n+1) for n!=1; ln(b/a) for n=-1, (1) where a, b, and x are real numbers and lnx is the natural logarithm.

The number of coincidences of a (nu,nu^') correspondence of value gamma on a curve of curve genus p is given by nu+nu^'+2pgamma.

The average of the values of the class limits for a given class. A class mark is also called a midvalue or central value (Kenney and Keeping 1962, p. 14), and is commonly ...

A set within which the values of a function lie (as opposed to the range, which is the set of values that the function actually takes).

The comass of a differential p-form phi is the largest value of phi on a p vector of p-volume one, sup_(v in ^ ^pTM,|v|=1)|phi(v)|.

A function f(x) is completely convex in an open interval (a,b) if it has derivatives of all orders there and if (-1)^kf^((2k))(x)>=0 for k=0, 1, 2, ... in that interval ...

The difference of two complex numbers z=x+iy and z^'=x^'+iy^' is given by z-z^'=(x-x^')+i(y-y^'). In component form, (x,y)-(x^',y^')=(x-x^',y-y^').

The concatenation of two strings a and b is the string ab formed by joining a and b. Thus the concatenation of the strings "book" and "case" is the string "bookcase". The ...

A polynomial P(x) that, when evaluated over each x in the domain of definition, results in the same value. The simplest example is P(x)=c for x in R and c a constant.

A curve in two dimensions on which the value of a function f(x,y) is a constant. Other synonymous terms are equipotential curve, isarithm, and isopleth. A plot of several ...