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  2. Probability-generating function - Wikipedia

    en.wikipedia.org/wiki/Probability-generating...

    Probability generating functions are often employed for their succinct description of the sequence of probabilities Pr(X = i) in the probability mass function for a random variable X, and to make available the well-developed theory of power series with non-negative coefficients.

  3. Generating function - Wikipedia

    en.wikipedia.org/wiki/Generating_function

    Unlike an ordinary series, the formal power series is not required to converge: in fact, the generating function is not actually regarded as a function, and the "variable" remains an indeterminate. One can generalize to formal power series in more than one indeterminate, to encode information about infinite multi-dimensional arrays of numbers.

  4. Power series - Wikipedia

    en.wikipedia.org/wiki/Power_series

    The partial sums of a power series are polynomials, the partial sums of the Taylor series of an analytic function are a sequence of converging polynomial approximations to the function at the center, and a converging power series can be seen as a kind of generalized polynomial with infinitely many terms. Conversely, every polynomial is a power ...

  5. Frobenius method - Wikipedia

    en.wikipedia.org/wiki/Frobenius_method

    Some solutions of a differential equation having a regular singular point with indicial roots = and .. In mathematics, the method of Frobenius, named after Ferdinand Georg Frobenius, is a way to find an infinite series solution for a linear second-order ordinary differential equation of the form ″ + ′ + = with ′ and ″.

  6. List of PDF software - Wikipedia

    en.wikipedia.org/wiki/List_of_PDF_software

    Proprietary software for viewing and editing PDF documents. pdftk: GNU GPL/Proprietary: command-line tools to manipulate, edit and convert documents; supports filling of PDF forms with FDF/XFDF data. PDF-XChange Viewer: Freeware: Freeware PDF reader, tagger, editor (simple editions) and converter (free for non-commercial uses).

  7. List of mathematical series - Wikipedia

    en.wikipedia.org/wiki/List_of_mathematical_series

    An infinite series of any rational function of can be reduced to a finite series of polygamma functions, by use of partial fraction decomposition, [8] as explained here. This fact can also be applied to finite series of rational functions, allowing the result to be computed in constant time even when the series contains a large number of terms.

  8. Power series solution of differential equations - Wikipedia

    en.wikipedia.org/wiki/Power_series_solution_of...

    In order for the solution method to work, as in linear equations, it is necessary to express every term in the nonlinear equation as a power series so that all of the terms may be combined into one power series. As an example, consider the initial value problem ″ + ′ + ′ =; = , ′ = which describes a solution to capillary-driven flow in ...

  9. Formal power series - Wikipedia

    en.wikipedia.org/wiki/Formal_power_series

    A formal power series can be loosely thought of as an object that is like a polynomial, but with infinitely many terms.Alternatively, for those familiar with power series (or Taylor series), one may think of a formal power series as a power series in which we ignore questions of convergence by not assuming that the variable X denotes any numerical value (not even an unknown value).