Robert M. Corless
Junrui Hu
Abstract
We consider, from a symbolic point of view, a pair of definite integrals containing Lambert W, recently considered from a numerical point of view by Walter Gautschi. We transform the integrals to a shape that can be integrated in special cases by a computer-algebra system or by using tables of integrals, such as Prudnikov et al.
- Robert M. Corless, Gaston H. Gonnet, D. E. G. Hare, David J. Jeffrey, and Donald E. Knuth. On the Lambert W function. Advances in Computational Mathematics, 5:329--359, 1996.Google Scholar
Cross Ref
- Robert M. Corless and David J. Jeffrey. The Lambert W function. In N. J. Higham, editor, The Princeton Companion to Applied Mathematics. Princeton University Press, 2014.Google Scholar
- Steven R. Finch. Mathematical Constants, volume 96 of Encyclopedia of Mathematics and Its Applications. Cambridge University Press, 2003.Google Scholar
- Walter Gautschi. The Lambert W-functions and some of their integrals: a case study of high-precision computation. Numerical Algorithms, 57(1):27--34, 2011. Google ScholarDigital Library
- K. O. Geddes and G. J. Fee. Hybrid symbolic-numeric integration in Maple. In P. S. Wang, editor, Proceedings of ISSAC'92, pages 36--41. ACM Press, 1992. Google ScholarDigital Library
- Ronald L. Graham, Donald E. Knuth, and Oren Patashnik. Concrete Mathematics. Addison-Wesley, Boston, 1994.Google Scholar
- William B. Jordan and M. L. Glasser. Solution of problem 68-17. SIAM Review, 12(1):153--154, January 1970.Google ScholarDigital Library
- Frank W. J. Olver, Daniel W. Lozier, and Ronald F. Boisvert. NIST Handbook of Mathematical Functions. Cambridge University Press, 2010. Google ScholarDigital Library
- A. P. Prudnikov, Yu. A. Brychkov, and O. I. Marichev. Integrals and Series. Gordon & Breach, 1992.Google Scholar
Index Terms
- Some definite integrals containing the Tree T function
Recommendations
A certain class of incomplete elliptic integrals and associated definite integrals
In many seemingly diverse physical contexts (including, for example, certain radiation field problems, studies of crystallographic minimal surfaces, the theory of scattering of acoustic or electromagnetic waves by means of an elliptic disk, studies of ...
Asymptotic representations for hypergeometric-Bessel type function and fractional integrals
The paper is devoted to the study of asymptotic relations for the function λγ,σ(β)(z)=β/Γ(γ+1-1/β) ∫1∞ (tβ - 1)γ-1/βtσ e-ztdt generalising Tricomi confluent hypergeometric function and modified Bessel function of the third kind. The full asymptotic ...
Integrals involving a function associated with the Euler-Maclaurin summation formula
The authors first evaluate sums of certain series involving the Riemann Zeta function by using the theory of the double Gamma function. With or without the use of these results, the authors then establish seberal integrals involving a certain periodic ...
Comments