勒奇超越函数
特例编辑
积分形式编辑
级数展开编辑
参考文献编辑
- Apostol, T. M., Lerch's Transcendent, (编) Olver, Frank W. J.; Lozier, Daniel M.; Boisvert, Ronald F.; Clark, Charles W., 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. (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).