×
Choi, Junesang; Srivastava, H. M.

Integral representations for the Euler-Mascheroni constant \(\gamma \). (English) Zbl 1203.11085

Integral Transforms Spec. Funct. 21, No. 9-10, 675-690 (2010).
Authors’ abstract: Since the time of Euler, the so-called Euler-Mascheroni constant \(\gamma \) has been involved in a wide variety of important mathematical formulas and results. Among these formulas and results, a considerably large number of integral representations of \(\gamma \) have been developed. Here we aim at investigating several further integral expressions for the Euler-Mascheroni constant \(\gamma \).
Reviewer: Jürgen Hinz (Marburg)

Cited in 13 Documents

MSC:

11Y60 Evaluation of number-theoretic constants
11M35 Hurwitz and Lerch zeta functions
11M06 \(\zeta (s)\) and \(L(s, \chi)\)
33C05 Classical hypergeometric functions, \({}_2F_1\)

Keywords:

Euler-Mascheroni constant; gamma function; psi function; digamma function; Riemann zeta function; Hurwitz zeta function; generalized zeta function; Bernoulli numbers; Bernoulli polynomials; harmonic numbers; residue calculus
Cite Review PDF
Full Text: DOI

References:

[1] DOI: 10.2307/2315803 · Zbl 0153.09102 · doi:10.2307/2315803
[2] DOI: 10.1016/j.jmaa.2005.06.059 · Zbl 1093.33010 · doi:10.1016/j.jmaa.2005.06.059
[3] DOI: 10.2307/2975387 · doi:10.2307/2975387
[4] Appell P., C. R. Acad. Sci. Paris Sér. I Math. 15 pp 897– (1926)
[5] DOI: 10.1007/BF03024176 · Zbl 0558.01014 · doi:10.1007/BF03024176
[6] Brown J. W., Complex Variables and Applications,, 7. ed. (2003)
[7] Campbell R., Les Intégrals Eulériennes Et Leurs Applications (1966)
[8] Carrier G. F., Functions of a Complex Variable: Theory and Technique (1983) · Zbl 0548.30001
[9] DOI: 10.1080/10652460903064216 · Zbl 1188.33003 · doi:10.1080/10652460903064216
[10] Choi, J.Integral and series representations for the Euler’s constant. Proceedings of the Seventh Conference on Real and Complex Analysis (. October15–162003), Hiroshima, Japan. pp.43–55. Hiroshima: Hiroshima University.
[11] Choi, J. and Lee, J.Closed-form evaluation of a class of series associated with the Riemann zeta function. Proceedings of the Eleventh International Conference on Finite or Infinite Dimensional Complex Analysis and Applications (. July27–312003), Chiang Mai, Thailand. pp.36–53. Chiang Mai: Chiang Mai University.
[12] Choi J., Comm. Korean Math. Soc. 13 pp 683– (1998)
[13] Choi J., Indian J. Pure Appl. Math. 30 pp 649– (1999)
[14] Choi J., East Asian Math. J. 18 pp 75– (2002)
[15] DOI: 10.1006/jmaa.1997.5198 · Zbl 0869.11067 · doi:10.1006/jmaa.1997.5198
[16] DOI: 10.1080/10652460902943519 · Zbl 1242.33002 · doi:10.1080/10652460902943519
[17] DOI: 10.2996/kmj/1050496647 · Zbl 1040.11062 · doi:10.2996/kmj/1050496647
[18] DOI: 10.2307/2975308 · doi:10.2307/2975308
[19] Edwards, H. M. 2001. ”Riemann’s Zeta Function”. Mineola, New York: Dover Publications. · Zbl 1113.11303
[20] DOI: 10.1017/CBO9780511550447 · doi:10.1017/CBO9780511550447
[21] DOI: 10.2307/2316370 · Zbl 0174.09503 · doi:10.2307/2316370
[22] Glaisher J. W.L., Messenger Math. 1 pp 25– (1872)
[23] Gradshteyn I. S., Tables of Integrals, Series, and Products,, 6. ed. (2000) · Zbl 0981.65001
[24] Hansen E. R., A Table of Series and Products (1975) · Zbl 0438.00001
[25] Hardy G. H., An Introduction to the Theory of Numbers (1954) · Zbl 0058.03301
[26] Havil J., Gamma (Exploring Euler’s Constant) (2003) · Zbl 1023.11001
[27] DOI: 10.1090/S0002-9904-1902-00923-3 · JFM 33.0976.07 · doi:10.1090/S0002-9904-1902-00923-3
[28] Knopp K., Theory and Application of Infinite Series (1951) · Zbl 0042.29203
[29] Knuth D. E., Math. Comput. 16 pp 275– (1962)
[30] L. Mascheroni,Adnotationes ad calculum integralem Euleri, Vols. 1 and 2, Ticino, Italy, 1790 and 1792. Reprinted in L. Euler,Leonhardi Euleri Opera Omnia, Ser. 1, Vol. 12, B.G. Teubner, Leipzig, 1915, 415–542
[31] Ramanujan S., J. Indian Math. Soc. 3 pp 209– (1911)
[32] Ramanujan S., Messenger Math. 46 pp 73– (1916)
[33] Riemann B., Monatsber. Akad. Berlin 1859 pp 671– (1859)
[34] DOI: 10.2307/30037385 · Zbl 1138.11356 · doi:10.2307/30037385
[35] Srivastava H. M., Riv. Mat. Univ. Parma (Ser. 4) 14 pp 1– (1988)
[36] DOI: 10.1016/0022-247X(88)90013-3 · Zbl 0632.10040 · doi:10.1016/0022-247X(88)90013-3
[37] Srivastava H. M., Series Associated with the Zeta and Related Functions (2001) · Zbl 1014.33001 · doi:10.1007/978-94-015-9672-5
[38] Vacca G., Quart. J. Pure Appl. Math. 41 pp 363– (1910)
[39] Walfisz, A. 1963.Weylsche Exponentialsummen in der Neueren Zahlentheorie, 114–115. Leipzig: B. G. Teubner. · Zbl 0146.06003
[40] Wells, D. 1986.The Penguin Dictionary of Curious and Interesting Numbers, 28Middlesex, England: Penguin Books.
[41] Whittaker E. T., A Course of Modern Analysis: An Introduction to the General Theory of Infinite Processes and of Analytic Functions; With an Account of the Principal Transcendental Functions,, 4. ed. (1963)
[42] DOI: 10.2307/2974795 · doi:10.2307/2974795
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.