Some New Transformation Properties of the Nielsen Generalized Polylogarithm
Many of the properties of Nielsen generalized polylogarithm Sn,p(z), for example, the special value and the transformation formulas, play important roles in the computation of higher order radiative corrections in quantum electrodynamics. In this paper, some transformation formulas of z→p(z),p(z)=1-...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2014/210890 |
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| _version_ | 1832553747661717504 |
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| author | Nina Shang Qinghua Feng Huizeng Qin |
| author_facet | Nina Shang Qinghua Feng Huizeng Qin |
| author_sort | Nina Shang |
| collection | DOAJ |
| description | Many of the properties of Nielsen generalized polylogarithm Sn,p(z), for example, the special value and the transformation formulas, play important roles in the computation of higher order radiative corrections in quantum electrodynamics. In this paper, some transformation formulas of z→p(z),p(z)=1-z,1/z,1/(1-z),z/(z-1), and (1-z)/z are obtained. In particular, the last three transformation formulas are new results so far in the literature. By use of these transformation formulas presented, new fast algorithms for Nielsen generalized polylogarithm Sn,p(z) can be designed. For sn,p=Sn,p(1), a new recurrence formula is also given. The identities and the calculation of σn,p and an,p are also investigated. |
| format | Article |
| id | doaj-art-5e0a39248313471d8d3d03e70661b2ab |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-5e0a39248313471d8d3d03e70661b2ab2025-02-03T05:53:24ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252014-01-01201410.1155/2014/210890210890Some New Transformation Properties of the Nielsen Generalized PolylogarithmNina Shang0Qinghua Feng1Huizeng Qin2Institute of Applied Mathematics, Shandong University of Technology, Zibo, Shandong 255049, ChinaInstitute of Applied Mathematics, Shandong University of Technology, Zibo, Shandong 255049, ChinaInstitute of Applied Mathematics, Shandong University of Technology, Zibo, Shandong 255049, ChinaMany of the properties of Nielsen generalized polylogarithm Sn,p(z), for example, the special value and the transformation formulas, play important roles in the computation of higher order radiative corrections in quantum electrodynamics. In this paper, some transformation formulas of z→p(z),p(z)=1-z,1/z,1/(1-z),z/(z-1), and (1-z)/z are obtained. In particular, the last three transformation formulas are new results so far in the literature. By use of these transformation formulas presented, new fast algorithms for Nielsen generalized polylogarithm Sn,p(z) can be designed. For sn,p=Sn,p(1), a new recurrence formula is also given. The identities and the calculation of σn,p and an,p are also investigated.http://dx.doi.org/10.1155/2014/210890 |
| spellingShingle | Nina Shang Qinghua Feng Huizeng Qin Some New Transformation Properties of the Nielsen Generalized Polylogarithm International Journal of Mathematics and Mathematical Sciences |
| title | Some New Transformation Properties of the Nielsen Generalized Polylogarithm |
| title_full | Some New Transformation Properties of the Nielsen Generalized Polylogarithm |
| title_fullStr | Some New Transformation Properties of the Nielsen Generalized Polylogarithm |
| title_full_unstemmed | Some New Transformation Properties of the Nielsen Generalized Polylogarithm |
| title_short | Some New Transformation Properties of the Nielsen Generalized Polylogarithm |
| title_sort | some new transformation properties of the nielsen generalized polylogarithm |
| url | http://dx.doi.org/10.1155/2014/210890 |
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