Revision #559 → #1252 · back to history
addedGamma function (Euler integral)e252e487f6e6
addedReciprocal gamma is entire5b629d444339
addedGamma as Mellin transform of exponential decay3f70087f036e
addedInterpolation problem for factorial59f162f63a71
addedPseudogamma functionc84fff766658
addedFunctional equation interpolating shifted factorial98f1121423ed
addedBohr–Mollerup theorem52403b3606a6
addedEuler integral of the second kinda05de230683f
addedRecurrence via integration by parts3d8a72f8223e
addedGamma equals factorial at positive integersaf56a3cf7b78
addedAnalytic continuation via functional identity145d5539b349
addedEuler's infinite product definitiond320eef18100
addedReciprocal as entire infinite productab2a9eb07db6
addedWeierstrass's definition78c812afa6fa
addedEquivalence of integral and Weierstrass definitions49f1ec525a0d
addedEquivalence of Weierstrass and Euler definitionsef706be2534f
addedEuler's reflection formula7c4828441121
addedLegendre duplication formula90774bd7661a
addedMultiplication theorem731ee7061aca
addedProperty from limit definitionbf31c197c8a8
addedClosed form at integer/half-integer real part16e4bf0a0c83
addedReflection applied to specific argumentf0b796a92b03
addedValue of Gamma(1/2)5c7b12d633d5
addedTranscendence of Gamma at rationals8ae4fc79a4e9
addedDerivatives via polygamma function8a67e54e4543
addedDerivative at positive integersf5c7b9005386
addednth derivative formula41c182474e00
addedLaurent series expansion633a88d931c4
addedStrict logarithmic convexityce0ef0231d48
addedJensen-type inequality from log-convexity22650e588f51
addedGautschi's inequality09a656a50b8a
addedStirling's formula092576203921
addedAsymptotic limit for Gammacdc87ff6191a
addedStirling product definitiondc92c7d64fbc
addedExtension to negative non-integer valuese356e449d81b
addedMeromorphic with simple poles at non-positive integers1f907e843c56
addedResidue at a simple pole69f2b3a916c4
addedResidues of the gamma function5da19777d508
addedReciprocal gamma is entire with specified zeros63e6b68f16ef
addedLocal minimum on real line89af1e1b53da
addedSolution to Gamma(z-0.5)=Gamma(z+0.5)2ab4a6239846
addedSign alternation between polesab870e0c71b5
addedAlternative integral representationsef53e2e08a89
addedBinet's first integral formula9d9510b39d47
addedBinet's second integral formula0eb82a860b4b
addedHankel's formulaa93bc219d9d9
addedContinued fraction representationc81bcc0166b6
addedKummer/Malmsten Fourier series for log Gammafd3ae36ca7fe
addedRaabe's formula183c8f4316dd
addedGauss's Pi function93d50ae360bf
addedReflection and multiplication via Pi85bea676e27e
addedVolume of n-ellipsoid5aca1338283c
addedUpper incomplete gamma function839911014f7a
addedBeta–Gamma relation03ce4f4a7bf5
addedDigamma function31c2e398259f
addedRelation to Riemann zeta6f1d5aa5126e
addedLerch's formula for log Gamma4854401eba54
addedMoments of stretched exponentialf9c6a563bd08
addedParticular values of the gamma functionb0f4772971f9
addedLog-gamma functionc5af602876f4
addedFunctional equation for log-gamma318f2a19b71d
addedRocktaeschel's approximation589cd52a5811
addedBöhmer's approximation833dbb078f05
addedHermite's Stirling series96f033dccc3f
addedBohr–Mollerup theorem (Properties)515652c88866
addedWielandt theoremec86c624a5d5
addedUnique simultaneous characterization68ede42e43f8
addedTaylor series of log Gamma around 163b288b8c70f
addedIntegral representation for log-gamma083a5c5417eb
addedLog-gamma formula at rationals33f5529a43e0
addedIntegral of log-gamma via Barnes G9a9bd9ff6cd0
addedIntegral of log-gamma via Hurwitz zetab17666e15ef4
addedEspinosa–Moll integral of squared log-gammab3cbde9cdbf6
addedBailey et al. evaluation40f12818402b
addedLanczos approximatione02ea8e85a9d
addedFixed precision computation via integration by parts71751b56c6cf
addedTranslation property for tables925290a725d6
addedPower-times-linear integral evaluation95de53de812c
addedBinomial coefficient via gamma2f00bfa64fc4
addedProducts of rational functions via gammab1c55aeb416a
addedRiemann zeta functional equationa352b15100b6
addedBernoulli's product representation3dc0c5b64d4e
addedEuler's infinite product (historical)2fa399e7147c
addedEuler's integral representation (historical)be89dd38aa69
addedGauss's rewriting of Euler's productf76d563d48c0
addedWeierstrass's product representation23c94273d347
addedWeierstrass factorization theoremcfbbe8fdbf05
addedHölder's theoremb1f84ed46ec6
addedBohr–Mollerup theorem (historical)bc99d5f67cee