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Function Equal to Its Derivative

An alternative representation of the last integral can be expressed in plane polar coordinates r, 0. The two coordinate systems are related by [Pg.9]

The element of area in polar coordinates is given by rdrdO, so that the double integral becomes [Pg.9]

Integration over 9 gives a factor In. The integral over r can be done after the substitution u = j, du = Irdr  [Pg.9]

Therefore, = 2n x = it, and Laplace s result (1.22) follows from the square root. [Pg.9]

The problem is to find a function /(x) that is equal to its own derivative / (x). Assume that /(x) can be expressed as a power series [Pg.9]


See other pages where Function Equal to Its Derivative is mentioned: [Pg.9]    [Pg.9]   


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Derivative function

Equal

Equaling

Equality

Equalization

Function derived

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