Bibliography for the Residue Calculus

unabridged

 

  1. Residue Theorem and Theta Function Identities
    Liu Z-G.
    The Ramanujan Journal, June 2001, vol. 5, no. 2, pp. 129-151(23), Ingenta.  
  2. Residue theorem and related integrals
    De Oliveira E.C.
    International Journal of Mathematical Education in Science and Technology, 1 January 2001, vol. 32, no. 1, pp. 156-160(5), Ingenta.  
  3. Single-channel correlators and residue calculus
    Jacob P.; Mathieu P.
    Journal of Physics A: Mathematical and General, 2001, vol. 34, no. 47, pp. 10141-10158(18), Ingenta.  
  4. Use of the residue theorem to invert Laplace transforms
    Loney, N.W.
    Chemical Engineering Education, v 35, n 1, Winter, 2001, p 22-24, Engr.Village.    
  5. Test for properness using residue calculus.
    Adornato, Daniela; Fabiano, Adelina
    Rend. Circ. Mat. Palermo (2) 50 (2001), no. 1, 171--176, MathSciNet.  
  6. Calcul fonctionnel sous-elliptique et résidu non commutatif sur les variétés de Heisenberg. (French) [Subelliptic functional calculus and noncommutative residue on Heisenberg manifolds]
    Ponge, Raphaël
    C. R. Acad. Sci. Paris Sér. I Math. 332 (2001), no. 7, 611--614, MathSciNet.  
  7. A Residue Calculus for Root Systems
    van den Ban E.P.; Schlichtkrull H.
    Compositio Mathematica, August 2000, vol. 123, no. 1, pp. 27-72(46), Ingenta.   
  8. Residue calculus with differential operator.
    Nakamura, Yayoi; Tajima, Shinichi
    Kyushu J. Math. 54 (2000), no. 1, 127--138, MathSciNet.  
  9. Multivariable residue calculation algorithms that use partial differential operators and the Chinese remainder theorem. (Japanese)
    Tajima, Shinichi
    Theory and application in computer algebra (Japanese) (Kyoto, 2000). Surikaisekikenkyusho Kokyuroku No. 1199 (2001), 51--69, MathSciNet.  
  10. Residue Calculus and Effective Nullstellensatz  
    Carlos A. Berenstein; Alain Yger  
    American Journal of Mathematics, Vol. 121, No. 4. (Aug., 1999), pp. 723-796, Jstor.  
  11. Precision solution to symmetrical inductive discontinuities of finite thickness in the parallel-plate waveguides using the modified residue-calculus method
    Shibazaki, Toshihiko; Kinoshita, Teruhiro
    IEICE Transactions on Electronics, v E81-C, n 12, Dec, 1998, p 1807-1813, Engr.Village.    
  12. A Study on the Epstein-Hubbell Generalized Elliptic-Type Integral Using Residue Theory
    Cengiz A.
    Applied Mathematics and Computation, April 1997, vol. 83, no. 1, pp. 19-26(8), Ingenta.  
  13. Remarks on the analytic implicit function theorem
    Berger, Erich
    Journal of Mathematical Analysis and Applications, v 209, n 2, May 15, 1997, p 435-439, Engr.Village.    
  14. Comparison of the parabolic approximation with residue calculus in ocean acoustics.
    Buchanan, James L.; Gilbert, Robert P.
    Generalized analytic functions (Graz, 1997), 241--253, Int. Soc. Anal. Appl. Comput., 1, Kluwer Acad. Publ., Dordrecht, 1998, MathSciNet.  
  15. A generalization of the basic theorem on residues and its application. (Chinese)
    Jiang, Run Rong
    Math. Practice Theory 27 (1997), no. 4, 354--360, MathSciNet.  
  16. Numerical analysis of capacitive discontinuities of finite thickness in rectangular waveguides using the modified residue-calculus method
    Shibazaki, Toshihiko; Kinoshita, Teruhiro;  Shibamoto, Takeharu
    IEICE Transactions on Electronics, v E79-C, n 10, Oct, 1996, p 1391-1398, Engr.Village.    
  17. Regarding the calculus of real integrals using the residue theorem.  
    Popovici, Florin; Anisca, Ruazvan; Bencze, Mihály
    Octogon Math. Mag.  4  (1996),  no. 2, 21--23. 26A09
  18. Transcendental singular integrals and a generalized residue theorem. (Chinese)
    Zhong, Shou Guo
    Acta Math. Sci. (Chinese) 15 (1995), no. 1, 43--48, MathSciNet.  
  19. Numerical analysis of inductive discontinuities of finite thickness in rectangular waveguides using the modified residue-calculus method
    Shibazaki, Toshihiko; Kinoshita, Teruhiro;  Shin'yagaito, Ryoji
    IEICE Transactions on Electronics, v E77-C, n 11, Nov, 1994, p 1786-1794, Engr.Village.   
  20. Computing Schubert's calculus with Severi residues: an introduction to quantum cohomology.
    Bertram, Aaron
    Moduli of vector bundles (Sanda, 1994; Kyoto, 1994), 1--10, Lecture Notes in Pure and Appl. Math., 179, Dekker, New York, 1996, MathSciNet.
  21. A generalized residue theorem for unbounded multiply connected regions of the second class. (Chinese)
    Zhong, Shou Guo
    Acta Math. Sci. (Chinese) 14 (1994), no. 2, 163--167, MathSciNet.  
  22. A multidimensional version of the Cauchy residue theorem. (Russian)
    Sklyarenko, E. G.
    Mat. Zametki 49 (1991), no. 3, 109--113, 160; translation in Math. Notes 49 (1991), no. 3-4, 302--304, MathSciNet.  
  23. Global residue theorem on analytic varieties
    Hatziafratis, Telemachos E.
    Journal of Mathematical Analysis and Applications, v 149, n 2, Jul 1, 1990, p 475-488, Engr.Village.    
  24. Le calcul des résidus et ses applications à la théorie des fonctions. (French) [The calculus of residues and its applications to the theory of functions]
    Lindelöf, Ernst
    Reprint of the 1905 original. Les Grands Classiques Gauthier-Villars. [Gauthier-Villars Great Classics] Éditions Jacques Gabay, Sceaux, 1989. viii+145 pp., MathSciNet.  
  25. Calcul de résidus et problèmes de division. (French) [Residue calculus and division problems]
    Berenstein, Carlos A.; Yger, Alain
    C. R. Acad. Sci. Paris Sér. I Math. 308 (1989), no. 6, 163--166, MathSciNet.  
  26. The Cauchy theorem and residues of an analytic function in domains with a quasiconformal boundary. (Russian)
    Batchaev, I. M.
    Izv. Severo-Kavkaz. Nauchn. Tsentra Vyssh. Shkoly Estestv. Nauk. 1988, no. 4, 57--60, 143, MathSciNet.  
  27. Diffraction Of A Plane Wave By A Thick Strip Grating - Application Of The Modified Residue Calculus Technique.
    Kobayashi, Kazuya; Miura, Katsutoshi
    AP-S International Symposium (Digest) IEEE Antennas and Propagation Society, 1987, p 718-721, Engr.Village.    
  28. A local analogon of the theorem for the complete sum of residues.
    Yuzhakov, A. P.
    Complex analysis and applications '87 (Varna, 1987), 560--563, Publ. House Bulgar. Acad. Sci., Sofia, 1989, MathSciNet.  
  29. Modified Residue Calculus Technique For Microstrip Step Discontinuities.
    Chu, T. S.; Itoh, T.
    Electronics Letters, v 21, n 7, Mar 28, 1985, p 257-258, Engr.Village.    
  30. Analysis Of Microstrip Step Discontinuity By The Modified Residue Calculus Technique.
    Chu, Tak Sum; Itoh, Tatsuo
    IEEE Transactions on Microwave Theory and Techniques, v MTT-33, n 10, Oct, 1985, p 1024-1028, Engr.Village.    
  31. Two simple proofs of the theorem for the maximal domain of univalence of the class of rational functions with simple poles and positive residues.
    Todorov, P. G.
    C. R. Acad. Bulgare Sci. 37 (1984), no. 4, 429--432, MathSciNet.  
  32. The application of the residue theorem to the study of a finite queue with batch Poisson arrivals and synchronous servers.
    Chang, Jin Fu; Chang, Rong Feng
    SIAM J. Appl. Math. 44 (1984), no. 3, 646--656, MathSciNet.  
  33. Extensions of several summation formulae of Ramanujan using the calculus of residues.
    Forrester, Peter J.
    Rocky Mountain J. Math. 13 (1983), no. 4, 557--572, MathSciNet.  
  34. Erweiterung eines Satzes von Schinzel über Potenzreste. (German) [Extension of a theorem of Schinzel on power residues]
    Schulze, Volker
    Acta Arith. 41 (1982), no. 4, 383--394, MathSciNet.   
  35. Calcul des résidus en analyse p-adique, d'après Gerritzen et van der Put. (French) [Calculus of residues in p-adic analysis, following Gerritzen and van der Put]
    Robba, Philippe
    Study group on ultrametric analysis, 9th year: 1981/82, No. 2, Exp. No. 28, 8 pp., Inst. Henri Poincaré, Paris, 1983, MathSciNet.  
  36. Théorèmes de Gauss-Bonnet, de Hopf, et résidus des connexions métriques à singularités. (French) [Theorems of Gauss-Bonnet and Hopf, and residues of metric connections with singularities]
    Lehmann, Daniel
    Enseign. Math. (2) 27 (1981), no. 1-2, 41--55, MathSciNet.  
  37. Electromagnetic Boundary-Value Problems Based Upon A Modification Of Residue Calculus And Function Theoretic Techniques.
    Montgomery, James Patrick;   Chang, David C.  Source:
    NBS Monograph (United States), n 164, Jun, 1979, 183p, Engr.Village.    
  38. Theorem on the full sum of residues in CPn. (Russian)
    Cih, A. K.
    Uspekhi Mat. Nauk 34 (1979), no. 6(210), 207--210, MathSciNet.  
  39. Residue-Calculus Solution Of The Tm10-Mode Problem In Circular Corrugated Waveguides.
    Al-Hakkak, M. J.
    Proceedings of the Institution of Electrical Engineers (London), v 125, n 9, Sep, 1978, p 787-792, Engr.Village.    
  40. Cauchyjevravcun ostataka sa primenama. (Serbo-Croatian) [Cauchy's calculus of residues with applications] Matemativcki Problemi i Ekspozicije. 8. [Mathematical Problems and Expositions. 8.]
    Mitrinovi'c, Dragoslav S.; Kevcki'c, Jovan D.
    Nauvcna Kniga, Belgrade, 1978. 271 pp., MathSciNet.  
  41. A generalized residue theorem and its applications. (Chinese)
    Lu, Jian Ke
    Wuhan Daxue Xuebao 1978, no. 3, 1--8, MathSciNet.  
  42. Calculus of residues and general Cauchy formulas in Cn.
    Aronszajn, Nachman
    Bull. Sci. Math. (2) 101 (1977), no. 4, 319--352, MathSciNet.  
  43. A remark on the residue theorem of Bott.
    Heitsch, James L.
    Indiana Univ. Math. J. 25 (1976), no. 12, 1139--1147, MathSciNet.  
  44. Classical theorems on quadratic residues.  
    Berndt, Bruce C.
    Enseignement Math. (2)  22  (1976), no. 3--4, 261--304, MathSciNet.  
  45. The Residue Calculus in Several Complex Variables  
    Gerald Leonard Gordon  
    Transactions of the American Mathematical Society, Vol. 213. (Nov., 1975), pp. 127-176, Jstor.  
  46. Residue And Partial Fraction Evaluations Of Distributed And Lumped System Functions With Multiple Order Poles.
    Lindsay, James E. Jr.
    IEEE Transactions on Education, v E-18, n 2, May, 1975, p 100-105, Engr.Village.    
  47. An operator residue theorem with applications to branching processes and renewal type integral equations.
    Schumitzky, Alan; Wenska, Tom
    SIAM J. Math. Anal. 6 (1975), 229--235, MathSciNet.  
  48. Algorithm For Residue And Partial Fraction Evaluation Of Distributed And Lumped System Functions With Multiple Order Poles.
    Lindsay, J. E. Jr.
    Research Report - New York State Department of Transportation, Engineering Research and Development Bureau, 1974, p 199-204, Engr.Village.  
  49. The residue calculus in several complex variables. Fonctions de plusieurs variables complexes (Sém. François Norguet, 1970--1973; à la mémoire d'André Martineau), pp. 430--438.
    Gordon, Gerald
    Lecture Notes in Math., Vol. 409, Springer, Berlin, 1974, MathSciNet.  
  50. Summation of Series by the Residue Theorem  
    Henry J. Ricardo  
    Mathematics Magazine, Vol. 44, No. 1. (Jan., 1971), pp. 24-26, Jstor.  
  51. An operator generalization of the logarithmic residue theorem and Rouché's theorem. (Russian)
    Gohberg, I. C.; Sigal, E. I.
    Mat. Sb. (N.S.) 84(126) (1971), 607--629, MathSciNet.  
  52. A modified residue calculus technique.
    Mittra, R.; Lee, S. W.; Vanblaricum, G. F.
    Internat. J. Engrg. Sci. 6 1968 395--408, MathSciNet.  
  53. The residue calculus and some transcendental results in algebraic geometry. I, II.
    Griffiths, Phillip A.
    Proc. Nat. Acad. Sci. U.S.A. 55 1966 1303--1309; 1392--1395, MathSciNet.  
  54. Calculus of residues. In cooperation with J. H. Michael.
    Mitrinovi'c, D. S.
    Tutorial Text No. 4 P. Noordhoff Ltd., Groningen 1966 87 pp., MathSciNet.  
  55. Note on Evaluating Certain Real Integrals by Cauchy's Residue Theorem (in Classroom Notes)  
    Orin J. Farrell  
    American Mathematical Monthly, Vol. 68, No. 2. (Feb., 1961), pp. 151-152, Jstor.  
  56. Introduction to the residue calculus.
    van der Corput, J. G.
    Nederl. Akad. Wetensch. Proc. Ser. A 64 = Indag. Math. 23 1961 143--156, MathSciNet.  
  57. A Residue Theorem for Finite Blaschke Products  
    Maurice Heins  
    Proceedings of the American Mathematical Society, Vol. 2, No. 4. (Aug., 1951), pp. 622-624, Jstor.  
  58. Residue theorems of harmonic functions of three variables.
    Bergman, Stefan
    Bull. Amer. Math. Soc. 49, (1943). 163--174, MathSciNet.  

 

 

 Return to the Complex Analysis Project

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2003