Best example is that an "odd" (or "even") function's Maclaurin series only has terms with odd (or even) powers. cos(x) and sin(x) are examples of odd and even functions with easy to calculate Maclaurin series.
Yes. If the Maclaurin expansion of a function locally converges to the function, then you know the function is smooth. In addition, if the residual of the Maclaurin expansion converges to 0, the function is analytic.
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Its periodicity and amplitude remain the same.
Properties of elements are a periodic function of their atomic masses.
A graph has two axes, X and Y. A function can be seen on the graph based on the formula with X and Y representing certain properties in the formula.
Yes. If the Maclaurin expansion of a function locally converges to the function, then you know the function is smooth. In addition, if the residual of the Maclaurin expansion converges to 0, the function is analytic.
A maclaurin series is an expansion of a function, into a summation of different powers of the variable, for example x is the variable in ex. The maclaurin series would give the exact answer to the function if the series was infinite but it is just an approximation. Examples can be found on the site linked below.
Sinc function is a cosine cardinal function
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Mendeleev was the first to notice that properties of elements exist as a perdoic function of atomic mass
The official definition for the word wave function is "a function that satisfies a wave equation and describes the properties of a wave."
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Unless the number happens to be a straightforward power of the base of the logs, the answer is that you cannot without some access to tables or a scientific calculator. There are Maclaurin series for the log function but without a powerful calculator, you will not get far with them.
Properties of elements are periodic function of atomic number. Elements with same chemical properties are grouped together.
A black-box function is a function whose closed-form expression is not known or does not exist, and whose properties cannot be inferred.