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Exponential functions with bases 2 and 1/2. In mathematics, the exponential function is the unique real function which maps zero to one and has a derivative equal to its value. . The exponential of a variable is denoted or , with the two notations used interchangeab
The definition of e x as the exponential function allows defining b x for every positive real numbers b, in terms of exponential and logarithm function. Specifically, the fact that the natural logarithm ln(x) is the inverse of the exponential function e x means that one has = () = for every b > 0.
The physicist Richard Feynman called the equation "our jewel" and "the most remarkable formula in mathematics". [ 2 ] When x = π , Euler's formula may be rewritten as e iπ + 1 = 0 or e iπ = −1 , which is known as Euler's identity .
The most efficient algorithms allow solving easily (on a computer) polynomial equations of degree higher than 1,000 (see Root-finding algorithm). For polynomials with more than one indeterminate, the combinations of values for the variables for which the polynomial function takes the value zero are generally called zeros instead of "roots".
This list of mathematical series contains formulae for finite and infinite sums. It can be used in conjunction with other tools for evaluating sums. Here, is taken to have the value
In mathematics and computational science, the Euler method (also called the forward Euler method) is a first-order numerical procedure for solving ordinary differential equations (ODEs) with a given initial value.
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