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rwooduk
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- 59
Please delete, got mixed up, apologies.
phyzguy said:I think you are confused. This approximation is for [itex] \hbar \omega << kT[/itex].
The exponential function, denoted as f(x) = ex, is a mathematical function that describes the growth of a quantity over time. It is characterized by a rapid increase in value as the input variable (x) increases.
The expansion of the exponential function is a mathematical process of rewriting the exponential function in a series form, where the powers of the base (e) are expanded into a sum of terms. This expansion allows for easier manipulation and calculation of the function.
The expansion of the exponential function is useful because it allows for the simplification of complex exponential expressions. It also helps in solving differential equations, determining the limit of functions, and in various other mathematical applications.
The general form of the expansion of the exponential function is given by f(x) = ex = 1 + x + x2/2! + x3/3! + x4/4! + ... + xn/n!, where n is the number of terms in the expansion.
Some common properties of the expansion of the exponential function include: the coefficient of xn is always 1/n!, the expansion is valid for all real values of x, the expansion is an infinite series, and the expansion converges to the original exponential function as the number of terms increases.