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Also, characterisations (1), (2), and (4) for apply directly for a complex number. Definition (3) presents a problem because there are non-equivalent paths along which one could integrate; but the equation of (3) should hold for any such path modulo .
1.3 Chemistry. 1.4 Biology. 1.5 Economics. 2 Other equations. Toggle Other equations subsection. 2.1 Mathematics. 2.2 Physics. ... Equation solving; Theory of equations
It is also possible to take the variable y to be the unknown, and then the equation is solved by y = x – 1. Or x and y can both be treated as unknowns, and then there are many solutions to the equation; a symbolic solution is (x, y) = (a + 1, a), where the variable a may take any value. Instantiating a symbolic solution with specific numbers ...
According to this definition, E[X] exists and is finite if and only if E[X +] and E[X −] are both finite. Due to the formula |X| = X + + X −, this is the case if and only if E|X| is finite, and this is equivalent to the absolute convergence conditions in the definitions above. As such, the present considerations do not define finite ...
[4] This will not work if squares or higher power of x occurs in an exponent, or if the "base constants" do not "share" a common q. sometimes, substituting y=xe x may obtain an algebraic equation; after the solutions for y are known, those for x can be obtained by applying the Lambert W function, [citation needed] e.g.:
1.4 Other integrals. 2 Definite integrals. ... In the following formulas, ... The last expression is the logarithmic mean.
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In all cases, there is a parameter value or array of parameter values that solves one or more linear equations derived from the exponent terms of the integrand's series expansion. Consecutive integer exponents, 1 variable