Exponential Function - Formal Definition

Formal Definition

The exponential function ex can be characterized in a variety of equivalent ways. In particular it may be defined by the following power series:

Using an alternate definition for the exponential function leads to the same result when expanded as a Taylor series.

Less commonly, ex is defined as the solution y to the equation

It is also the following limit:

Read more about this topic:  Exponential Function

Famous quotes containing the words formal and/or definition:

    The manifestation of poetry in external life is formal perfection. True sentiment grows within, and art must represent internal phenomena externally.
    Franz Grillparzer (1791–1872)

    ... if, as women, we accept a philosophy of history that asserts that women are by definition assimilated into the male universal, that we can understand our past through a male lens—if we are unaware that women even have a history—we live our lives similarly unanchored, drifting in response to a veering wind of myth and bias.
    Adrienne Rich (b. 1929)