Editing Polylogarithm (section)

==References==
{{Reflist}}
{{refbegin}}
* {{cite book | last= Abel | first= N.H. | author-link= Niels Henrik Abel | contribution= Note sur la fonction <math>\scriptstyle \psi x = x+ \frac{x^2}{2^2}+ \frac{x^3}{3^2}+ \cdots+ \frac{x^n}{n^2}+ \cdots</math> | language= fr | contribution-url= http://www.abelprisen.no/nedlastning/verker/oeuvres_1881_del2/oeuvres_completes_de_abel_nouv_ed_2_kap14_opt.pdf | contribution-format= PDF | editor1-last= Sylow | editor1-first= L. | editor2-last= Lie | editor2-first= S. | title= Œuvres complètes de Niels Henrik Abel − Nouvelle édition, Tome II | location= Christiania [Oslo] | publisher= Grøndahl & Søn | orig-year= 1826 | year= 1881 | pages= 189–193 }} (this 1826 manuscript was only published posthumously.)
* {{cite book | last1= Abramowitz | first1= M. | last2= Stegun | first2= I.A. | title= Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables | location= New York | publisher= Dover Publications | year= 1972 | isbn= 978-0-486-61272-0 | title-link= Abramowitz and Stegun }}
* {{dlmf | id= 25.12 | first= T.M. | last= Apostol }}
* {{cite journal | last1= Bailey | first1= D.H. | author1-link= David H. Bailey (mathematician) | last2= Borwein | first2= P.B. | author2-link= Peter Borwein | last3= Plouffe | first3= S. | author3-link= Simon Plouffe | title= On the Rapid Computation of Various Polylogarithmic Constants | url= http://crd.lbl.gov/~dhbailey/dhbpapers/digits.pdf | journal= Mathematics of Computation |date=April 1997 | volume= 66 | issue= 218 | pages= 903–913 | doi= 10.1090/S0025-5718-97-00856-9 | bibcode= 1997MaCom..66..903B| doi-access= free }}
* {{cite arXiv | last1= Bailey | first1= D.H. | last2= Broadhurst | first2= D.J. | title= A Seventeenth-Order Polylogarithm Ladder | eprint= math.CA/9906134 | date= June 20, 1999 }}
* {{cite book | last= Berndt | first= B.C. | title= Ramanujan's Notebooks, Part IV | location= New York | publisher= Springer-Verlag | year= 1994 | pages= 323–326 | isbn=978-0-387-94109-7 }}
* {{cite journal | author-link= Johannes Boersma | last1= Boersma | first1= J. | last2= Dempsey | first2= J.P. | title= On the evaluation of Legendre's chi-function | jstor= 2152987 | journal= Mathematics of Computation | year= 1992 | volume= 59 | issue= 199 | pages= 157–163 | doi= 10.2307/2152987 | url= https://research.tue.nl/nl/publications/on-the-numerical-evaluation-of-legendres-chifunction(cb45fc94-8446-4b7f-80f8-7bf3b220e62e).html }}
* {{cite journal | last1= Borwein | first1= D. | author1-link= David Borwein | last2= Borwein | first2= J.M. | author2-link= Jonathan Borwein | last3= Girgensohn | first3= R. | title= Explicit evaluation of Euler sums | url= http://docserver.carma.newcastle.edu.au/58/2/93_001-Borwein-Borwein-Girgensohn.pdf | journal= Proceedings of the Edinburgh Mathematical Society |series=Series 2 | year= 1995 | volume= 38 | issue= 2 | pages= 277–294 | doi= 10.1017/S0013091500019088 | doi-access= free }}
* {{cite journal | last1= Borwein | first1= J.M. | last2= Bradley | first2= D.M. | last3= Broadhurst | first3= D.J. | last4= Lisonek | first4= P. | title= Special Values of Multiple Polylogarithms | journal= Transactions of the American Mathematical Society | year= 2001 | volume= 353 | issue= 3 | pages= 907–941 | doi= 10.1090/S0002-9947-00-02616-7 | arxiv= math/9910045 | s2cid= 11373360 }}
* {{cite arXiv | last= Broadhurst | first= D.J. | title= On the enumeration of irreducible k-fold Euler sums and their roles in knot theory and field theory | eprint= hep-th/9604128 | date= April 21, 1996 }}
* {{cite journal | last= Clunie | first= J. | title= On Bose-Einstein functions | journal= Proceedings of the Physical Society | series = Series A | year= 1954 | volume= 67 | issue= 7 | pages= 632–636 | doi= 10.1088/0370-1298/67/7/308 | bibcode= 1954PPSA...67..632C }}
* {{cite journal | last1= Cohen | first1= H. | last2= Lewin | first2= L. | last3= Zagier | first3= D. | title= A Sixteenth-Order Polylogarithm Ladder | url= http://www.expmath.org/expmath/volumes/1/1.html | format= PS | journal= Experimental Mathematics | year= 1992 | volume= 1 | issue= 1 | pages= 25–34 }}
* {{cite journal | last= Coxeter | first= H.S.M. | author-link= Harold Scott MacDonald Coxeter | title= The functions of Schläfli and Lobatschefsky | journal= Quarterly Journal of Mathematics | year= 1935 | volume= 6 | issue= 1 | pages= 13–29 | doi= 10.1093/qmath/os-6.1.13 | jfm= 61.0395.02 | bibcode= 1935QJMat...6...13C }}
* {{cite journal | last1= Cvijovic | first1= D. | last2= Klinowski | first2= J. | title= Continued-fraction expansions for the Riemann zeta function and polylogarithms | url= https://www.ams.org/journals/proc/1997-125-09/S0002-9939-97-04102-6/S0002-9939-97-04102-6.pdf | journal= Proceedings of the American Mathematical Society | year= 1997 | volume= 125 | issue= 9 | pages= 2543–2550 | doi= 10.1090/S0002-9939-97-04102-6 | doi-access= free }}
* {{cite journal | last= Cvijovic | first= D. | title= New integral representations of the polylogarithm function | journal= [[Proceedings of the Royal Society A]] | year= 2007 | volume= 463 | issue= 2080 | pages= 897–905 | doi= 10.1098/rspa.2006.1794 | arxiv= 0911.4452 | bibcode= 2007RSPSA.463..897C | s2cid= 115156743 }}
* {{Cite journal |last=Dingle |first=R. B. |date=1955 |title=The evaluation of integrals containing a parameter |url=http://link.springer.com/10.1007/BF02920017 |journal=Applied Scientific Research, Section B |language=en |volume=4 |issue=1 |pages=401–410 |doi=10.1007/BF02920017 |issn=0365-7140}}
* {{Cite journal |last=Dingle |first=R. B. |date=1957a |title=The Bose-Einstein integrals <math>\mathcal{B}_p (\eta ) = (p!)^{ - 1} \int\limits_0^\infty {\varepsilon ^p (e^{\varepsilon - \eta } - 1} )^{ - 1} d\varepsilon </math> |url=http://link.springer.com/10.1007/BF02920380 |journal=Applied Scientific Research, Section B |language=en |volume=6 |issue=1 |pages=240–244 |doi=10.1007/BF02920380 |issn=0365-7140}}
* {{Cite journal |last=Dingle |first=R. B. |last2=Arndt |first2=Doreen |last3=Roy |first3=S. K. |date=1957 |title=The integrals <math>\mathfrak{A}_p (x) = (p!)^{ - 1} \int\limits_0^\infty {\varepsilon ^p (\varepsilon + x} )^{ - 1} e^{ - \varepsilon } d\varepsilon</math> and <math>\mathfrak{B}_p (x) = (p!)^{ - 1} \int\limits_0^\infty {\varepsilon ^p (\varepsilon + x} )^{ - 2} e^{ - \varepsilon } d\varepsilon</math> and their tabulation |url=http://link.springer.com/10.1007/BF02920371 |journal=Applied Scientific Research, Section B |language=en |volume=6 |issue=1 |pages=144–154 |doi=10.1007/BF02920371 |issn=0365-7140}}
* {{Cite journal |last=Dingle |first=R. B. |date=1957b |title=The Fermi-Dirac integrals <math>\mathcal{F}_p (\eta ) = (p!)^{ - 1} \int\limits_0^\infty {\varepsilon ^p (e^{\varepsilon - \eta } + 1} )^{ - 1} d\varepsilon </math> |url=http://link.springer.com/10.1007/BF02920379 |journal=Applied Scientific Research, Section B |language=en |volume=6 |issue=1 |pages=225–239 |doi=10.1007/BF02920379 |issn=0365-7140}}
* {{cite book | last1= Erdélyi | first1= A. | author1-link= Arthur Erdélyi | last2= Magnus | first2= W. | last3= Oberhettinger | first3= F. | last4= Tricomi | first4= F.G. | title= Higher Transcendental Functions, Vol. 1 | url= https://s3.amazonaws.com/apps.nrbook.com/bateman/Vol1.pdf | location= Malabar, FL | publisher= R.E. Krieger Publishing | year= 1981 | isbn= 978-0-89874-206-0 | ref= {{harvid|Erdélyi et al.|1981}}}} (this is a reprint of the McGraw–Hill original of 1953.)
* {{cite journal | last1= Fornberg | first1= B. | last2= Kölbig | first2= K.S. | title= Complex zeros of the Jonquière or polylogarithm function | jstor= 2005579 | journal= Mathematics of Computation | year= 1975 | volume= 29 | issue= 130 | pages= 582–599 | doi= 10.2307/2005579 | url= https://cds.cern.ch/record/880364 }}
* {{cite web | author= GNU Scientific Library | url= https://www.gnu.org/software/gsl/manual/gsl-ref.html#SEC117 | title= Reference Manual | year= 2010 | access-date= 2010-06-13 | ref= {{harvid|GSL|2010}} }}
*{{cite book
 | last1 = Gradshteyn | first1 = I. S.
 | last2 = Ryzhik | first2 = I. M.
 | contribution = 9.55 The function <math>\Phi(z,s,v)</math>: Series representation 9.553, 9.554
 | contribution-url = https://books.google.com/books?id=F7jiBQAAQBAJ&pg=PA1075
 | edition = 7th<!-- as numbered by MathSciNet -->
 | isbn = 978-0-12-384933-5
 | mr = 3307944
 | page = 1075
 | publisher = Elsevier/Academic Press | location = Amsterdam
 | title = Table of Integrals, Series, and Products
 | title-link = Gradshteyn and Ryzhik
 | year = 2015}}
* {{cite journal | last1= Guillera | first1= J. | last2= Sondow | first2= J. | title= Double integrals and infinite products for some classical constants via analytic continuations of Lerch's transcendent | arxiv= math.NT/0506319 | journal= The Ramanujan Journal | year= 2008 | volume= 16 | issue= 3 | pages= 247–270 | doi= 10.1007/s11139-007-9102-0 | s2cid= 119131640 }}
* {{cite arXiv | last= Hain | first= R.M. | title= Classical polylogarithms | eprint= alg-geom/9202022 | date= March 25, 1992 }}
* {{cite book | last1= Jahnke | first1= E. | last2= Emde | first2= F. | title= Tables of Functions with Formulae and Curves | edition= 4th | location= New York | publisher= Dover Publications | year= 1945 }}
* {{cite journal | last= Jonquière | first= A. | title= Note sur la série <math>\scriptstyle \sum_{n=1}^\infty \frac{x^n}{n^s}</math> | language= fr | url= http://archive.numdam.org/item?id=BSMF_1889__17__142_1 | format= PDF | journal= Bulletin de la Société Mathématique de France | year= 1889 | volume= 17 | pages= 142–152 | jfm= 21.0246.02 | doi= 10.24033/bsmf.392 | doi-access= free }}
* {{cite journal | last1= Kölbig | first1= K.S. | last2= Mignaco | first2= J.A. | last3= Remiddi | first3= E. | title= On Nielsen's generalized polylogarithms and their numerical calculation | journal= BIT | year= 1970 | volume= 10 | pages= 38–74 | doi= 10.1007/BF01940890 | s2cid= 119672619 | url= https://cds.cern.ch/record/350733 }}
* {{cite journal | last= Kirillov | first= A.N. | title= Dilogarithm identities | arxiv= hep-th/9408113 | journal= Progress of Theoretical Physics Supplement | year= 1995 | volume= 118 | pages= 61–142 | doi= 10.1143/PTPS.118.61 | bibcode= 1995PThPS.118...61K | s2cid= 119177149 }}
* {{cite book | last= Lewin | first= L. | title= Dilogarithms and Associated Functions | location= London | publisher= Macdonald | year= 1958 | mr= 0105524 }}
* {{cite book | last= Lewin | first= L. | title= Polylogarithms and Associated Functions | location= New York | publisher= North-Holland | year= 1981 | isbn= 978-0-444-00550-2 }}
* {{cite book | editor-last= Lewin | editor-first= L. | title= Structural Properties of Polylogarithms | series= Mathematical Surveys and Monographs | volume= 37 | location= Providence, RI | publisher= Amer. Math. Soc. | year= 1991 | isbn= 978-0-8218-1634-9 }}
* {{cite journal | last= Markman | first= B. | title= The Riemann Zeta Function | journal= BIT | year= 1965 | volume= 5 | pages= 138–141 }}
* {{cite journal | last= Maximon | first= L.C. | title= The Dilogarithm Function for Complex Argument | journal= [[Proceedings of the Royal Society A]] | year= 2003 | volume= 459 | issue= 2039 | pages= 2807–2819 | doi= 10.1098/rspa.2003.1156 | bibcode= 2003RSPSA.459.2807M | s2cid= 122271244 }}
* {{cite journal | last1= McDougall | first1= J. | last2= Stoner | first2= E.C. | title= The computation of Fermi-Dirac functions | journal= [[Philosophical Transactions of the Royal Society A]] | year= 1938 | volume= 237 | issue= 773 | pages= 67–104 | doi= 10.1098/rsta.1938.0004 | jfm= 64.1500.04 | bibcode= 1938RSPTA.237...67M | doi-access= free }}
* {{cite journal | author-link= Niels Nielsen (mathematician) | last= Nielsen | first= N. | title= Der Eulersche Dilogarithmus und seine Verallgemeinerungen. Eine Monographie | language= de | location= Halle – Leipzig, Germany | publisher= Kaiserlich-Leopoldinisch-Carolinische Deutsche Akademie der Naturforscher | journal= Nova Acta Leopoldina | year= 1909 | volume= XC | issue= 3 | pages= 121–212 | jfm= 40.0478.01 }}
* {{cite book | last1= Prudnikov | first1= A.P. | last2= Marichev | first2= O.I. | last3= Brychkov | first3= Yu.A. | title= Integrals and Series, Vol. 3: More Special Functions | location= Newark, NJ | publisher= Gordon and Breach | year= 1990 | isbn= 978-2-88124-682-1 }} (see § 1.2, "The generalized zeta function, Bernoulli polynomials, Euler polynomials, and polylogarithms", p.&nbsp;23.)
* {{cite journal | last= Robinson | first= J.E. | title= Note on the Bose-Einstein integral functions | journal= Physical Review | series = Series 2 | year= 1951 | volume= 83 | issue= 3 | pages= 678–679 | doi= 10.1103/PhysRev.83.678 | bibcode= 1951PhRv...83..678R }}
* {{cite journal | last= Rogers | first= L.J. | title= On function sum theorems connected with the series <math>\scriptstyle \sum_{n=1}^\infty \frac{x^n}{n^2}</math> | journal= Proceedings of the London Mathematical Society (2) | year= 1907 | volume= 4 | issue= 1 | pages= 169–189 | doi= 10.1112/plms/s2-4.1.169 | jfm= 37.0428.03 | url= https://zenodo.org/record/1447792 }}
* {{cite book | last= Schrödinger | first= E. | author-link= Erwin Schrödinger | title= Statistical Thermodynamics | edition= 2nd | location= Cambridge, UK | publisher= Cambridge University Press | year= 1952 }}
* {{cite journal | last= Truesdell | first= C. | title= On a function which occurs in the theory of the structure of polymers | jstor= 1969153 | journal= Annals of Mathematics |series=Second Series | year= 1945 | volume= 46 | issue= 1 | pages= 144–157 | doi= 10.2307/1969153 }}
* {{cite journal | last= Vepstas | first= L. | title= An efficient algorithm for accelerating the convergence of oscillatory series, useful for computing the polylogarithm and Hurwitz zeta functions | arxiv= math.CA/0702243 | journal= Numerical Algorithms | year= 2008 | volume= 47 | issue= 3 | pages= 211–252 | doi= 10.1007/s11075-007-9153-8 | bibcode= 2008NuAlg..47..211V | s2cid= 15131811 }}
* {{cite book | last1= Whittaker | first1= E.T. | author1-link= Edmund Taylor Whittaker | last2= Watson | first2= G.N. | author2-link= George Neville Watson | title= [[A Course of Modern Analysis]] | edition= 4th | location= Cambridge, UK | publisher= Cambridge University Press | year= 1927 }} (this edition has been reprinted many times, a 1996 paperback has {{isbn|0-521-09189-6}}.)
* {{cite journal | last= Wirtinger | first= W. | title= Über eine besondere Dirichletsche Reihe | language= de | journal= Journal für die Reine und Angewandte Mathematik | year= 1905 | volume= 1905 | issue= 129 | pages= 214–219 | jfm= 37.0434.01 | doi=10.1515/crll.1905.129.214| s2cid= 199545536 }}
* {{cite web | last= Wood | first= D.C. | title= The Computation of Polylogarithms. Technical Report 15-92* | url= http://www.cs.kent.ac.uk/pubs/1992/110 | format= PS | location= Canterbury, UK | publisher= University of Kent Computing Laboratory |date=June 1992 | access-date= 2005-11-01 }}
* {{cite conference | last= Zagier | first= D. | author-link= Don Zagier | title= The dilogarithm function in geometry and number theory | book-title= Number Theory and Related Topics: papers presented at the Ramanujan Colloquium, Bombay, 1988 | series= Studies in Mathematics | volume= 12 | location= Bombay | publisher= Tata Institute of Fundamental Research and Oxford University Press | year= 1989 | pages= 231–249 | isbn= 0-19-562367-3 }} (also appeared as "The remarkable dilogarithm" in ''Journal of Mathematical and Physical Sciences'' '''22''' (1988), pp.&nbsp;131–145, and as Chapter I of {{harv|Zagier|2007}}.)
* {{cite book | last= Zagier | first= D. | chapter= The Dilogarithm Function | chapter-url= http://mathlab.snu.ac.kr/~top/articles/zagier.pdf | editor1-last= Cartier | editor1-first= P.E. | editor2-last= Julia | editor2-first= B. | editor3-last= Moussa | editor3-first= P. | editor4-last= Vanhove | editor4-first= P. | display-editors= 1 | title= Frontiers in Number Theory, Physics, and Geometry II – On Conformal Field Theories, Discrete Groups and Renormalization | location= Berlin | publisher= Springer-Verlag | year= 2007 | pages= 3–65 | isbn= 978-3-540-30307-7 }}
{{refend}}