000 03103nam a22004455i 4500
001 978-3-0348-0431-8
003 DE-He213
005 20140220083254.0
007 cr nn 008mamaa
008 120913s2012 sz | s |||| 0|eng d
020 _a9783034804318
_9978-3-0348-0431-8
024 7 _a10.1007/978-3-0348-0431-8
_2doi
050 4 _aQA351
072 7 _aPBKF
_2bicssc
072 7 _aMAT034000
_2bisacsh
072 7 _aMAT037000
_2bisacsh
082 0 4 _a515.5
_223
100 1 _aErnst, Thomas.
_eauthor.
245 1 2 _aA Comprehensive Treatment of q-Calculus
_h[electronic resource] /
_cby Thomas Ernst.
264 1 _aBasel :
_bSpringer Basel :
_bImprint: Birkhäuser,
_c2012.
300 _aXVI, 495 p. 15 illus., 1 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
505 0 _a1 Introduction -- 2 The different languages of q -- 3 Pre q-Analysis -- 4 The q-umbral calculus and the semigroups. The Nørlund calculus of finite diff -- 5 q-Stirling numbers -- 6 The first q-functions -- 7 An umbral method for q-hypergeometric series -- 8 Applications of the umbral calculus -- 9 Ciglerian q-Laguerre polynomials -- 10 q-Jacobi polynomials -- 11 q-Legendre polynomials and Carlitz-AlSalam polynomials -- 12 q-functions of many variables -- 13 Linear partial q-difference equations -- 14 q-Calculus and physics -- 15 Appendix: Other philosophies.
520 _aTo date, the theoretical development of q-calculus has rested on a non-uniform basis. Generally, the bulky Gasper-Rahman notation was used, but the published works on q-calculus looked different depending on where and by whom they were written. This confusion of tongues not only complicated the theoretical development but also contributed to q-calculus remaining a neglected mathematical field. This book overcomes these problems by introducing a new and interesting notation for q-calculus based on logarithms. For instance, q-hypergeometric functions are now visually clear and easy to trace back to their hypergeometric parents. With this new notation it is also easy to see the connection between q-hypergeometric functions and the q-gamma function, something that until now has been overlooked. The book covers many topics on q-calculus, including special functions, combinatorics, and q-difference equations. Beyond a thorough review of the historical development of q-calculus, it also presents the domains of modern physics for which q-calculus is applicable, such as particle physics and supersymmetry, to name just a few.
650 0 _aMathematics.
650 0 _aFunctions, special.
650 0 _aNumber theory.
650 1 4 _aMathematics.
650 2 4 _aSpecial Functions.
650 2 4 _aNumber Theory.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783034804301
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-0348-0431-8
912 _aZDB-2-SMA
999 _c101748
_d101748