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A substitution which can be used to transform integrals involving square roots into a more tractable form. form substitution sqrt(x^2+a^2) x=asinhu sqrt(x^2-a^2) x=acoshu

Conditions at an initial time t=t_0 from which a given set of mathematical equations or physical system evolves. A system with initial conditions specified is known as an ...

A function for which the integral can be computed is said to be integrable.

Of all convex n-gons of a given perimeter, the one which maximizes area is the regular n-gon.

A point of discontinuity, also called a leap.

Laplace's integral is one of the following integral representations of the Legendre polynomial P_n(x), P_n(x) = 1/piint_0^pi(du)/((x+sqrt(x^2-1)cosu)^(n+1))du (1) = ...

A local extremum, also called a relative extremum, is a local minimum or local maximum.

A local maximum, also called a relative maximum, is a maximum within some neighborhood that need not be (but may be) a global maximum.

A local minimum, also called a relative minimum, is a minimum within some neighborhood that need not be (but may be) a global minimum.

A function is called locally integrable if, around every point in the domain, there is a neighborhood on which the function is integrable. The space of locally integrable ...