What organization did Carl Johan Malmsten join in 1882?
Carl Johan Malmsten Carl Johan Malmsten ( April 9 , 1814 in Uddetorp , Skara County , Sweden – February 11 , 1886 in Uppsala , Sweden ) was a Swedish mathematician and politician . He is notable for early research into the theory of functions of a complex variable , for the evaluation of several important logarithmic integrals and series , for his studies in the theory of Zeta-function related series and integrals , as well as for helping Mittag-Leffler start the journal Acta Mathematica . Malmsten became Docent in 1840 , and then , Professor of mathematics at the Uppsala University in 1842 . He was elected a member of the Royal Swedish Academy of Sciences in 1844 . He was also a minister without portfolio in 1859–1866 and Governor of Skaraborg County in 1866–1879 . Main contributions . Usually , Malmsten is known for his earlier works in complex analysis . However , he also greatly contributed in other branches of mathematics , but his results were undeservedly forgotten and many of them were erroneously attributed to other persons . Thus , it was comparatively recently that it was discovered by Iaroslav Blagouchine that Malmsten was first who evaluated several important logarithmic integrals and series , which are closely related to the gamma- and zeta-functions , and among which we can find the so-called Vardis integral and the Kummers series for the logarithm of the Gamma function . In particular , in 1842 he evaluated following lnln-logarithmic integrals The details and an interesting historical analysis are given in the Blagouchines paper . Many of these integrals were later rediscovered by various researchers , including Vardi , Adamchik , Medina and Moll . Moreover , some authors even named the first of these integrals after Vardi , who re-evaluated it in 1988 ( they call it Vardis integral ) , and so did many well-known internet resources such as Wolfram MathWorld site or OEIS Foundation site ( taking into account the undoubted Malmsten priority in the evaluation of such a kind of logarithmic integrals , it seems that the name Malmstens integrals would be more appropriate for them ) . Malmsten derived above formulae by making use of different series representations . At the same time , it has been shown that they can be also evaluated by methods of contour integration , by making use of the Hurwitz Zeta function , by employing polylogarithms and by using L-functions . More complicated forms of Malmstens integrals appear in works of Adamchik and Blagouchine ( more than 70 integrals ) . Below are several examples of such integrals where m and n are positive integers such that m<n , G - is the Catalans constant , ζ - stands for the Riemann zeta-function , Ψ - is the digamma function , Ψ - is the trigamma function ; see respectively eq . ( 43 ) , ( 47 ) and ( 48 ) in for the first three integrals , and exercises no . 36-a , 36-b , 11-b and 13-b in for the last four integrals respectively ( the third integral being calculated in both works ) . It is curious that some of Malmstens integrals lead to the gamma- and polygamma functions of a complex argument , which are not often encountered in analysis . For instance , as shown by Iaroslav Blagouchine , or , see exercises 7-а and 37 respectively . By the way , Malmstens integrals are also found to be closely connected to the Stieltjes constants . In 1842 , Malmsten also evaluated several important logarithmic series , among which we can find these two series The latter series was later rediscovered in a slightly different form by Ernst Kummer , who derived a similar expression in 1847 ( strictly speaking , the Kummers result is obtained from the Malmstens one by putting Moreover , this series is even known in analysis as Kummers series for the logarithm of the Gamma function , although Malmsten derived it 5 years before Kummer . Malsmten also notably contributed into the theory of zeta-function related series and integrals . In 1842 he proved following important functional relationship for the L-function as well as for the M-function where in both formulae 0Leonhard Euler</a> already in 1749 , but it was Malmsten who proved it ( Euler only suggested this formula and verified it for several integer and semi-integer values of s ) . Curiously enough , the same formula for L ( s ) was unconsciously rediscovered by Oscar Schlömilch in 1849 ( proof provided only in 1858 ) . Four years later , Malmsten derived several other similar reflection formulae , which turn out to be particular cases of the Hurwitzs functional equation . Speaking about the Malmstens contribution into the theory of zeta-functions , we can not fail to mention the very recent discovery of his authorship of the reflection formula for the first generalized Stieltjes constant at rational argument where m and n are positive integers such that m<n . This identity was derived , albeit in a slightly different form , by Malmsten already in 1846 and has been also discovered independently several times by various authors . In particular , in the literature devoted to Stieltjes constants , it is often attributed to Almkvist and Meurman who derived it in 1990s .