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Symbolab is an answer engine [1] that provides step-by-step solutions to mathematical problems in a range of subjects. [2] It was originally developed by Israeli start-up company EqsQuest Ltd., under whom it was released for public use in 2011. In 2020, the company was acquired by American educational technology website Course Hero. [3] [4]
The matrix exponential of another matrix (matrix-matrix exponential), [24] is defined as = = for any normal and non-singular n×n matrix X, and any complex n×n matrix Y. For matrix-matrix exponentials, there is a distinction between the left exponential Y X and the right exponential X Y , because the multiplication operator for matrix ...
The exponential of a variable is denoted or , with the two notations used interchangeably. It is called exponential because its argument can be seen as an exponent to which a constant number e ≈ 2.718, the base, is raised. There are several other definitions of the exponential function, which are all equivalent ...
Similar asymptotic analysis is possible for exponential generating functions; with an exponential generating function, it is a n / n! that grows according to these asymptotic formulae. Generally, if the generating function of one sequence minus the generating function of a second sequence has a radius of convergence that is larger than ...
The fractional Schrödinger equation, a fundamental equation of fractional quantum mechanics, has the following form: [69] [70] (,) = (,) + (,) (,). where the solution of the equation is the wavefunction ψ ( r , t ) – the quantum mechanical probability amplitude for the particle to have a given position vector r at any given time t , and ħ ...
In mathematics, a power series (in one variable) is an infinite series of the form = = + + + … where represents the coefficient of the nth term and c is a constant called the center of the series. Power series are useful in mathematical analysis , where they arise as Taylor series of infinitely differentiable functions .
In such graphs, exponential functions of the form f(x) = a · b x appear as straight lines with slope equal to the logarithm of b. Log-log graphs scale both axes logarithmically, which causes functions of the form f(x) = a · x k to be depicted as straight lines with slope equal to the exponent k. This is applied in visualizing and analyzing ...
One can attempt to use the definition of the Taylor series, though this often requires generalizing the form of the coefficients according to a readily apparent pattern. Alternatively, one can use manipulations such as substitution, multiplication or division, addition or subtraction of standard Taylor series to construct the Taylor series of a ...