He is notable for early research[1] 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.
Thus, it was comparatively recently that it was discovered by Iaroslav Blagouchine[3] 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 Vardi's integral and the Kummer's series for the logarithm of the Gamma function.
At the same time, it has been shown that they can be also evaluated by methods of contour integration,[3] by making use of the Hurwitz Zeta function,[5] by employing polylogarithms[6] and by using L-functions.
It is curious that some of Malmsten's integrals lead to the gamma- and polygamma functions of a complex argument, which are not often encountered in analysis.
[3][12][13][14] Four years later, Malmsten derived several other similar reflection formulae, which turn out to be particular cases of the Hurwitz's functional equation.
Speaking about the Malmsten's 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