Apostol, T. M., Lerch's Transcendent, Olver, Frank W. J.; Lozier, Daniel M.; Boisvert, Ronald F.; Clark, Charles W. (编), NIST Handbook of Mathematical Functions, Cambridge University Press, 2010, ISBN 978-0521192255, MR2723248.
Bateman, H.; Erdélyi, A., Higher Transcendental Functions, Vol. I (PDF), New York: McGraw-Hill, 1953 [2015-02-14], (原始内容 (PDF)于2011-08-11). (See § 1.11, "The function Ψ(z,s,v)", p. 27)
Gradshteyn, I.S.; Ryzhik, I.M., Tables of Integrals, Series, and Products 4th, New York: Academic Press, 1980, ISBN 0-12-294760-6. (see Chapter 9.55)
Guillera, Jesus; Sondow, Jonathan, Double integrals and infinite products for some classical constants via analytic continuations of Lerch's transcendent, The Ramanujan Journal, 2008, 16 (3): 247–270, MR 2429900, arXiv:math.NT/0506319, doi:10.1007/s11139-007-9102-0. (Includes various basic identities in the introduction.)
Jackson, M., On Lerch's transcendent and the basic bilateral hypergeometric series 2ψ2, J. London Math. Soc., 1950, 25 (3): 189–196, MR 0036882, doi:10.1112/jlms/s1-25.3.189.
Laurinčikas, Antanas; Garunkštis, Ramūnas, The Lerch zeta-function, Dordrecht: Kluwer Academic Publishers, 2002, ISBN 978-1-4020-1014-9, MR 1979048.
Lerch, Mathias, Note sur la fonction , Acta Mathematica, 1887, 11 (1–4): 19–24, JFM 19.0438.01, MR 1554747, doi:10.1007/BF02612318(法语).
十一月 02, 2023
勒奇超越函数, 是一种特殊函数, 推广了赫尔维茨ζ函数和多重对数函数, 定义如下lerch, transcendentlerch, plot, with, complex, variablel, displaystyle, infty, frac, 目录, 特例, 积分形式, 级数展开, 参考文献特例, 编辑赫尔维茨ζ函数, 当勒奇函数中的z, 1时, 化为赫尔维茨ζ函数, displaystyle, zeta, nbsp, 多重对数函数, 当勒奇函数中a, 则化为多重对数函数, displaystyle, nbs. 勒奇超越函数是一种特殊函数 推广了赫尔维茨z函数和多重对数函数 定义如下Lerch transcendentLerch plot with complex variableL z s a n 0 z n a n s displaystyle L z s a sum n 0 infty frac z n a n s 目录 1 特例 2 积分形式 3 级数展开 4 参考文献特例 编辑赫尔维茨z函数 当勒奇函数中的z 1时 化为赫尔维茨z函数 L 1 s a z s a displaystyle L 1 s a zeta s a nbsp 多重对数函数 当勒奇函数中a 1 则化为多重对数函数 L z s 1 L i s z displaystyle L z s 1 Li s z nbsp 勒让德x函数可以用勒奇超越函数表示 x n z 2 n z F z 2 n 1 2 displaystyle chi n z 2 n z Phi z 2 n 1 2 nbsp 作为赫尔维茨z函数的特例 黎曼z函数可以表示为 z s F 1 s 1 displaystyle zeta s Phi 1 s 1 nbsp 狄利克雷h函数可以表示为 h s F 1 s 1 displaystyle eta s Phi 1 s 1 nbsp 积分形式 编辑L z s a 1 G s 0 z x a x s d x displaystyle L z s a frac 1 Gamma s int 0 infty frac z x a x s dx nbsp 级数展开 编辑F z s q 1 1 z n 0 z 1 z n k 0 n 1 k n k q k s displaystyle Phi z s q frac 1 1 z sum n 0 infty left frac z 1 z right n sum k 0 n 1 k binom n k q k s nbsp 参考文献 编辑Apostol T M Lerch s Transcendent Olver Frank W J Lozier Daniel M Boisvert Ronald F Clark Charles W 编 NIST Handbook of Mathematical Functions Cambridge University Press 2010 ISBN 978 0521192255 MR2723248 Bateman H Erdelyi A Higher Transcendental Functions Vol I PDF New York McGraw Hill 1953 2015 02 14 原始内容存档 PDF 于2011 08 11 See 1 11 The function PS z s v p 27 Gradshteyn I S Ryzhik I M Tables of Integrals Series and Products 4th New York Academic Press 1980 ISBN 0 12 294760 6 see Chapter 9 55 Guillera Jesus Sondow Jonathan Double integrals and infinite products for some classical constants via analytic continuations of Lerch s transcendent The Ramanujan Journal 2008 16 3 247 270 MR 2429900 arXiv math NT 0506319 nbsp doi 10 1007 s11139 007 9102 0 Includes various basic identities in the introduction Jackson M On Lerch s transcendent and the basic bilateral hypergeometric series 2ps2 J London Math Soc 1950 25 3 189 196 MR 0036882 doi 10 1112 jlms s1 25 3 189 Laurincikas Antanas Garunkstis Ramunas The Lerch zeta function Dordrecht Kluwer Academic Publishers 2002 ISBN 978 1 4020 1014 9 MR 1979048 Lerch Mathias Note sur la fonction K w x s k 0 e 2 k p i x w k s displaystyle scriptstyle mathfrak K w x s sum k 0 infty e 2k pi ix over w k s nbsp Acta Mathematica 1887 11 1 4 19 24 JFM 19 0438 01 MR 1554747 doi 10 1007 BF02612318 法语 取自 https zh wikipedia org w index php title 勒奇超越函数 amp oldid 63378965, 维基百科,wiki,书籍,书籍,图书馆,