Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

On Stieltjes integral transforms involving $ \Gamma $-functions


Authors: V. Belevitch and J. Boersma
Journal: Math. Comp. 38 (1982), 223-226
MSC: Primary 44A15; Secondary 33A15, 33A45
MathSciNet review: 637300
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: After some methodological remarks on the theory of Stieltjes transforms, a systematic classification of transforms involving $ \Gamma $-functions is presented As a consequence, many new transforms are established and much simpler proofs for a few known transforms are obtained.


References [Enhancements On Off] (What's this?)

  • [1] V. Belevitch, ``On the realizability of non-rational positive real functions,'' Internat. J. Circuit Theory Appl., v. 1, 1973, pp. 17-30.
  • [2] Vitold Belevitch, The Gauss hypergeometric ratio as a positive real function, SIAM J. Math. Anal. 13 (1982), no. 6, 1024–1040. MR 674771 (83k:33002), http://dx.doi.org/10.1137/0513073
  • [3] V. V. Belevitch and J. Boersma, The Bessel ratio 𝐾_{𝜈+1}(𝑧)/𝐾_{𝜈}(𝑧) as a passive impedance, Philips J. Res. 34 (1979), no. 3-4, 163–173. MR 546260 (80f:94032)
  • [4] A. Erdélyi et al., Tables of Integral Transforms, Vol. 2, McGraw-Hill, New York, 1954.
  • [5] E. A. Guillemin, Theory of Linear Physical Systems, Wiley, New York, 1963, p. 552.
  • [6] N. Nielsen, Handbuch der Theorie der Gammafunktion, Chelsea, New York, 1965.
  • [7] D. F. Tuttle, Network Synthesis, Wiley, New York, 1958, p. 389.
  • [8] L. A. Zadeh & C. A. Desoer, Linear System Theory, McGraw-Hill, New York, 1963, p. 428.

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 44A15, 33A15, 33A45

Retrieve articles in all journals with MSC: 44A15, 33A15, 33A45


Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1982-0637300-3
PII: S 0025-5718(1982)0637300-3
Article copyright: © Copyright 1982 American Mathematical Society