KnowraGamma functionLinked fromLinked fromThe 25 pages that link to Gamma function, each with the reason it gives.All 25Broader topic 4Related 17Narrower topic 3Compared with 1Riemann zeta functionRelated: The gamma factor appears in the zeta function’s completed functional equation.Dedekind zeta functionRelated: Archimedean gamma factors complete the zeta function and produce its functional equation.Integration by partsRelated: Integration by parts yields the recurrence Γ(z+1)=zΓ(z) from its integral definition.Gaussian integralRelated: Its value at one half evaluates Gaussian integrals with powers of the variable.Mellin transformRelated: Its Mellin integral is a standard example and a recurring factor in transform formulas.Beta functionRelated: The beta function is a quotient of three gamma values.Negative binomial distributionRelated: It extends the distribution's combinatorial formula when its success parameter is generalized.Gamma distributionRelated: It normalizes the gamma density through the factor Γ(shape).Hadamard factorization theoremRelated: The reciprocal gamma function is entire and admits a canonical product that illustrates the theorem.Euler–Mascheroni constantRelated: The constant appears in expansions of the gamma function near zero and one.Integration by substitutionRelated: A variable change reduces a broad class of improper integrals to its defining integral.Class number formulaRelated: Archimedean gamma factors shape the completed zeta function whose pole is evaluated.Bohr–Mollerup theoremRelated: The theorem identifies this function as the unique one satisfying its hypotheses.Carlson's theoremRelated: Its integer values illustrate how discrete data can identify a function when growth conditions are available.Cauchy's formula for repeated integrationRelated: It replaces the factorial when the repeated-integration order is extended beyond integers.Deligne conjecture (critical L-values)Related: Gamma factors help determine which integers are critical and contribute archimedean normalizations.Dixon's identityRelated: The identity's closed form is a quotient of gamma-function values.
KnowraGamma functionLinked fromLinked fromThe 25 pages that link to Gamma function, each with the reason it gives.All 25Broader topic 4Related 17Narrower topic 3Compared with 1Riemann zeta functionRelated: The gamma factor appears in the zeta function’s completed functional equation.Dedekind zeta functionRelated: Archimedean gamma factors complete the zeta function and produce its functional equation.Integration by partsRelated: Integration by parts yields the recurrence Γ(z+1)=zΓ(z) from its integral definition.Gaussian integralRelated: Its value at one half evaluates Gaussian integrals with powers of the variable.Mellin transformRelated: Its Mellin integral is a standard example and a recurring factor in transform formulas.Beta functionRelated: The beta function is a quotient of three gamma values.Negative binomial distributionRelated: It extends the distribution's combinatorial formula when its success parameter is generalized.Gamma distributionRelated: It normalizes the gamma density through the factor Γ(shape).Hadamard factorization theoremRelated: The reciprocal gamma function is entire and admits a canonical product that illustrates the theorem.Euler–Mascheroni constantRelated: The constant appears in expansions of the gamma function near zero and one.Integration by substitutionRelated: A variable change reduces a broad class of improper integrals to its defining integral.Class number formulaRelated: Archimedean gamma factors shape the completed zeta function whose pole is evaluated.Bohr–Mollerup theoremRelated: The theorem identifies this function as the unique one satisfying its hypotheses.Carlson's theoremRelated: Its integer values illustrate how discrete data can identify a function when growth conditions are available.Cauchy's formula for repeated integrationRelated: It replaces the factorial when the repeated-integration order is extended beyond integers.Deligne conjecture (critical L-values)Related: Gamma factors help determine which integers are critical and contribute archimedean normalizations.Dixon's identityRelated: The identity's closed form is a quotient of gamma-function values.