Linked from

The 41 pages that link to Factorial, each with the reason it gives.

• Taylor seriesRelated: Dividing the nth derivative by n! gives the standard Taylor coefficient.

• Binomial coefficientRelated: The formula \(\binom{n}{k}=n!/(k!(n-k)!)\) computes the count.

• PermutationRelated: A set of n distinct elements has n! possible permutations.

• Binomial theoremRelated: Factorials provide a standard formula for binomial coefficients.

• Taylor's theoremRelated: Factorials normalize the derivative coefficients in the Taylor polynomial.

• Ratio testRelated: Factorials often make successive-term ratios simplify sharply in power series.

• Cauchy estimatesRelated: The nth-derivative bound contains n factorial from repeated differentiation of the integral formula.

• Euler's NumberRelated: The reciprocal factorials form e's power-series coefficients.

• OneRelated: Its boundary value of zero factorial is defined as one.

• Root testRelated: Nth roots of factorial expressions often simplify through Stirling's approximation.

• Rule of productRelated: Products of decreasing choices simplify to factorials when arranging distinct objects.

• Taylor polynomialRelated: Dividing the nth derivative by n! gives the standard Taylor coefficient.

• Abraham de MoivreRelated: De Moivre’s asymptotic approximation for factorials became a precursor to Stirling’s formula.

• Beta functionRelated: The gamma-function relationship makes beta values at integer arguments factorial ratios.

• CombinationRelated: Factorials express the number of arrangements and yield the combination formula.

• Exponential generating functionRelated: The denominator n! is the defining weight on the nth coefficient.

• Falling factorialRelated: For nonnegative integer x, the falling factorial of order x equals x!.

• Multinomial theoremRelated: Factorials express the theorem’s multinomial coefficients.

• Logarithmic differentiationRelated: Logarithmic derivatives describe its rate of relative change through the digamma function.

• Pascal's ruleRelated: Factorial formulas let the recurrence be checked directly from the definition of binomial coefficients.

• Binomial seriesRelated: Factorials appear in the coefficient denominators and connect them to ordinary binomial coefficients.

• Abel's binomial theoremRelated: Factorials define the binomial coefficients appearing in the expansion.

• Bohr–Mollerup theoremRelated: The recurrence and normalization reproduce factorial values at integer arguments.

• Highly composite numberRelated: Factorials are highly divisible, though usually not highly composite because smaller integers can tie or exceed their divisor counts.

• Leibniz formula for determinantsRelated: An n × n formula has n! permutation terms.

• Baranyai's theoremRelated: Factorials appear when counting partitions into equally sized, unlabeled blocks.

• BEST theoremRelated: The theorem’s local ordering choices appear as factorials of outdegrees.

• Cauchy's formula for repeated integrationRelated: The denominator n! normalizes the volume of the ordered integration region.

• Lah numberRelated: Factorials count arrangements and appear directly in the closed form.

• Proof that π is irrationalRelated: Rapid factorial growth makes the constructed integral small while preserving divisibility.