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  2. Binomial theorem - Wikipedia

    en.wikipedia.org/wiki/Binomial_theorem

    In elementary algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomial.According to the theorem, the power ⁠ (+) ⁠ expands into a polynomial with terms of the form ⁠ ⁠, where the exponents ⁠ ⁠ and ⁠ ⁠ are nonnegative integers satisfying ⁠ + = ⁠ and the coefficient ⁠ ⁠ of each term is a specific positive integer ...

  3. 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 ...

  4. General Leibniz rule - Wikipedia

    en.wikipedia.org/wiki/General_Leibniz_rule

    Relationship to the binomial theorem [ edit ] The Leibniz rule bears a strong resemblance to the binomial theorem , and in fact the binomial theorem can be proven directly from the Leibniz rule by taking f ( x ) = e a x {\displaystyle f(x)=e^{ax}} and g ( x ) = e b x , {\displaystyle g(x)=e^{bx},} which gives

  5. Falling and rising factorials - Wikipedia

    en.wikipedia.org/wiki/Falling_and_rising_factorials

    The falling factorial occurs in a formula which represents polynomials using the forward difference operator ⁡ = (+) , which in form is an exact analogue to Taylor's theorem: Compare the series expansion from umbral calculus

  6. Pascal's pyramid - Wikipedia

    en.wikipedia.org/wiki/Pascal's_pyramid

    Pascal's pyramid's first five layers. Each face (orange grid) is Pascal's triangle. Arrows show derivation of two example terms. In mathematics, Pascal's pyramid is a three-dimensional arrangement of the trinomial numbers, which are the coefficients of the trinomial expansion and the trinomial distribution. [1]

  7. Legendre's formula - Wikipedia

    en.wikipedia.org/wiki/Legendre's_formula

    Legendre's formula can be used to prove Kummer's theorem. As one special case, it can be used to prove that if n is a positive integer then 4 divides ( 2 n n ) {\displaystyle {\binom {2n}{n}}} if and only if n is not a power of 2.

  8. Category:Factorial and binomial topics - Wikipedia

    en.wikipedia.org/wiki/Category:Factorial_and...

    Beta negative binomial distribution; Bhargava factorial; Binomial (polynomial) Binomial approximation; Binomial coefficient; Binomial distribution; Binomial regression; Binomial series; Binomial theorem; Binomial transform; Binomial type; Brocard's problem

  9. Multinomial theorem - Wikipedia

    en.wikipedia.org/wiki/Multinomial_theorem

    In mathematics, the multinomial theorem describes how to expand a power of a sum in terms of powers of the terms in that sum. It is the generalization of the binomial theorem from binomials to multinomials .