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  2. Factorial - Wikipedia

    en.wikipedia.org/wiki/Factorial

    One property of the gamma function, distinguishing it from other continuous interpolations of the factorials, is given by the Bohr–Mollerup theorem, which states that the gamma function (offset by one) is the only log-convex function on the positive real numbers that interpolates the factorials and obeys the same functional equation.

  3. Table of Newtonian series - Wikipedia

    en.wikipedia.org/wiki/Table_of_Newtonian_series

    Download as PDF; Printable version; ... is the falling factorial. ... A proof for this identity can be obtained by showing that it satisfies the differential equation

  4. Runge–Kutta–Fehlberg method - Wikipedia

    en.wikipedia.org/wiki/Runge–Kutta–Fehlberg...

    Download as PDF; Printable version; In other projects ... "New high-order Runge-Kutta formulas with step size control for systems of first and second-order ...

  5. Yates analysis - Wikipedia

    en.wikipedia.org/wiki/Yates_Analysis

    Before performing a Yates analysis, the data should be arranged in "Yates' order". That is, given k factors, the k th column consists of 2 (k - 1) minus signs (i.e., the low level of the factor) followed by 2 (k - 1) plus signs (i.e., the high level of the factor).

  6. Legendre's formula - Wikipedia

    en.wikipedia.org/wiki/Legendre's_formula

    Since ! is the product of the integers 1 through n, we obtain at least one factor of p in ! for each multiple of p in {,, …,}, of which there are ⌊ ⌋.Each multiple of contributes an additional factor of p, each multiple of contributes yet another factor of p, etc. Adding up the number of these factors gives the infinite sum for (!

  7. Falling and rising factorials - Wikipedia

    en.wikipedia.org/wiki/Falling_and_rising_factorials

    These symbols are collectively called factorial powers. [2] The Pochhammer symbol, introduced by Leo August Pochhammer, is the notation (), where n is a non-negative integer. It may represent either the rising or the falling

  8. Stirling's approximation - Wikipedia

    en.wikipedia.org/wiki/Stirling's_approximation

    Comparison of Stirling's approximation with the factorial. In mathematics, Stirling's approximation (or Stirling's formula) is an asymptotic approximation for factorials. It is a good approximation, leading to accurate results even for small values of .

  9. Double factorial - Wikipedia

    en.wikipedia.org/wiki/Double_factorial

    These are counted by the double factorial 15 = (6 − 1)‼. In mathematics, the double factorial of a number n, denoted by n‼, is the product of all the positive integers up to n that have the same parity (odd or even) as n. [1] That is,

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