Editing Gamma function (section)

=== Fourier series expansion ===
The [[#Log-gamma function|logarithm of the gamma function]] has the following [[Fourier series]] expansion for <math>0 < z < 1:</math>
<math display="block">\operatorname{log\Gamma}(z) = \left(\frac{1}{2} - z\right)(\gamma + \log 2) + (1 - z)\log\pi - \frac{1}{2}\log\sin(\pi z) + \frac{1}{\pi}\sum_{n=1}^\infty \frac{\log n}{n} \sin (2\pi n z),</math>
which was for a long time attributed to [[Ernst Kummer]], who derived it in 1847.<ref>{{cite book|first1=Harry |last1=Bateman |first2=Arthur |last2=Erdélyi |title=Higher Transcendental Functions |publisher=McGraw-Hill |date=1955 |oclc=627135 }}</ref><ref>{{cite book|first1=H. M. |last1=Srivastava |first2=J. |last2=Choi |title=Series Associated with the Zeta and Related Functions |publisher=Kluwer Academic |location=The Netherlands |date=2001 |isbn=0-7923-7054-6 }}</ref> However, [[Iaroslav Blagouchine]] discovered that [[Carl Johan Malmsten]] first derived this series in 1842.<ref name="iaroslav_06">{{cite journal|doi=10.1007/s11139-013-9528-5 |first=Iaroslav V. |last=Blagouchine |title=Rediscovery of Malmsten's integrals, their evaluation by contour integration methods and some related results |journal=Ramanujan J. |volume=35 |issue=1 |pages=21–110 |date=2014 |s2cid=120943474 |url=https://www.researchgate.net/publication/257381156}}</ref><ref name="iaroslav_06bis">{{cite journal|doi=10.1007/s11139-015-9763-z |first=Iaroslav V. |last=Blagouchine |title=Erratum and Addendum to "Rediscovery of Malmsten's integrals, their evaluation by contour integration methods and some related results" |journal=Ramanujan J. |volume=42 |issue=3 |pages=777–781 |date=2016 |s2cid=125198685 }}</ref>