Logarithmic Integrals, Polylogarithmic Integrals and Euler sums

Relations among integrals of logarithms, polylogarithms and Euler sums are presented. A unifying element being the introduction of Nielsen’s generalized polylogarithms.

[1]  Pedro Freitas,et al.  Integrals of polylogarithmic functions, recurrence relations, and associated Euler sums , 2004, Math. Comput..

[2]  Mark W. Coffey,et al.  On one-dimensional digamma and polygamma series related to the evaluation of Feynman diagrams , 2005, math-ph/0505051.

[3]  K. S. Kolbig,et al.  Closed Expressions for Integral $t^{-1} \log^{(n-1)} t \log^p (1 - t) dt$ , 1982 .

[4]  K. S. Kölbig,et al.  Nielsen's generalized polylogarithms , 1986 .

[5]  EVALUATION OF SOME SIMPLE EULER-TYPE SERIES , 2009, 0912.3227.

[6]  P. Osland,et al.  Summing one- and two-dimensional series related to the Euler series , 1998, hep-th/9801168.

[7]  T. T. Wu,et al.  Expanding Protons: Scattering at High Energies , 1987 .

[8]  P. F. Jordan Infinite sums of psi functions , 1973 .

[9]  P. Osland,et al.  Some Infinite Series Related to Feynman Diagrams , 2000, math-ph/0010026.

[10]  Some definite logarithmic integrals from Euler sums, and other integration results , 2010, 1001.1366.

[11]  More series related to the Euler series , 1999, hep-th/9904206.

[12]  Michael Milgram On Some Sums of Digamma and Polygamma functions , 2004 .

[13]  N. Hofreiter,et al.  Der Eulersche Dilogarithmus und seine Verallgemeinerungen , 1973 .

[14]  Johannes Blumlein,et al.  Structural Relations of Harmonic Sums and Mellin Transforms at Weight w=6 , 2009, 0901.0837.

[15]  Károly Jordán Calculus of finite differences , 1951 .

[16]  Johannes Blümlein,et al.  Structural relations of harmonic sums and Mellin transforms up to weight w=5 , 2009, Comput. Phys. Commun..

[17]  Dennis W. Duke,et al.  Table of integrals and formulae for Feynman diagram calculations , 1983 .

[18]  Walter Troost,et al.  On the Evaluation of Polylogarithmic Integrals , 1980 .

[19]  L. Lewin,et al.  Dilogarithms and associated functions , 1958 .