On Stieltjes integral transforms involving $\Gamma$-functions
HTML articles powered by AMS MathViewer
- by V. Belevitch and J. Boersma PDF
- Math. Comp. 38 (1982), 223-226 Request permission
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
-
V. Belevitch, “On the realizability of non-rational positive real functions,” Internat. J. Circuit Theory Appl., v. 1, 1973, pp. 17-30.
- Vitold Belevitch, The Gauss hypergeometric ratio as a positive real function, SIAM J. Math. Anal. 13 (1982), no. 6, 1024–1040. MR 674771, DOI 10.1137/0513073
- V. V. Belevitch and J. Boersma, The Bessel ratio $K_{\nu +1}(z)/K_{\nu }(z)$ as a passive impedance, Philips J. Res. 34 (1979), no. 3-4, 163–173. MR 546260 A. Erdélyi et al., Tables of Integral Transforms, Vol. 2, McGraw-Hill, New York, 1954. E. A. Guillemin, Theory of Linear Physical Systems, Wiley, New York, 1963, p. 552. N. Nielsen, Handbuch der Theorie der Gammafunktion, Chelsea, New York, 1965. D. F. Tuttle, Network Synthesis, Wiley, New York, 1958, p. 389. L. A. Zadeh & C. A. Desoer, Linear System Theory, McGraw-Hill, New York, 1963, p. 428.
Additional Information
- © Copyright 1982 American Mathematical Society
- Journal: Math. Comp. 38 (1982), 223-226
- MSC: Primary 44A15; Secondary 33A15, 33A45
- DOI: https://doi.org/10.1090/S0025-5718-1982-0637300-3
- MathSciNet review: 637300