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  2. List of mathematical functions - Wikipedia

    en.wikipedia.org/wiki/List_of_mathematical_functions

    In mathematics, some functions or groups of functions are important enough to deserve their own names. This is a listing of articles which explain some of these functions in more detail. There is a large theory of special functions which developed out of statistics and mathematical physics.

  3. Factorial - Wikipedia

    en.wikipedia.org/wiki/Factorial

    In mathematical analysis, factorials are used in power series for the exponential function and other functions, and they also have applications in algebra, number theory, probability theory, and computer science. Much of the mathematics of the factorial function was developed beginning in the late 18th and early 19th centuries.

  4. Falling and rising factorials - Wikipedia

    en.wikipedia.org/wiki/Falling_and_rising_factorials

    A similar result holds for the rising factorial and the backward difference operator. The study of analogies of this type is known as umbral calculus. A general theory covering such relations, including the falling and rising factorial functions, is given by the theory of polynomial sequences of binomial type and Sheffer sequences. Falling and ...

  5. List of factorial and binomial topics - Wikipedia

    en.wikipedia.org/wiki/List_of_factorial_and...

    This is a list of factorial and binomial topics in mathematics. See also binomial (disambiguation). Abel's binomial theorem; Alternating factorial; Antichain; Beta function; Bhargava factorial; Binomial coefficient. Pascal's triangle; Binomial distribution; Binomial proportion confidence interval; Binomial-QMF (Daubechies wavelet filters ...

  6. Bhargava factorial - Wikipedia

    en.wikipedia.org/wiki/Bhargava_factorial

    The factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n. For example, 5! = 5×4×3×2×1 = 120. By convention, the value of 0! is defined as 1. This classical factorial function appears prominently in many theorems in number theory. The following are a few of these theorems. [1]

  7. Double factorial - Wikipedia

    en.wikipedia.org/wiki/Double_factorial

    I propose to write !! for such products, and if a name be required for the product to call it the "alternate factorial" or the "double factorial". Meserve (1948) [ 9 ] states that the double factorial was originally introduced in order to simplify the expression of certain trigonometric integrals that arise in the derivation of the Wallis product .

  8. q-Pochhammer symbol - Wikipedia

    en.wikipedia.org/wiki/Q-Pochhammer_symbol

    This is an analytic function of q in the interior of the unit disk, and can also be considered as a formal power series in q. The special case ϕ ( q ) = ( q ; q ) ∞ = ∏ k = 1 ∞ ( 1 − q k ) {\displaystyle \phi (q)=(q;q)_{\infty }=\prod _{k=1}^{\infty }(1-q^{k})} is known as Euler's function , and is important in combinatorics , number ...

  9. List of types of functions - Wikipedia

    en.wikipedia.org/wiki/List_of_types_of_functions

    Special functions: non-elementary functions that have established names and notations due to their importance. Trigonometric functions : relate the angles of a triangle to the lengths of its sides. Nowhere differentiable function called also Weierstrass function : continuous everywhere but not differentiable even at a single point.