메뉴 건너뛰기




Volumn 222, Issue 1, 1998, Pages 79-91

Solutions of Linear Difference Equations with Variable Coefficients

Author keywords

Linear difference equation; variable coefficients; explicit solution; companion matrices

Indexed keywords


EID: 0000651502     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmaa.1997.5903     Document Type: Article
Times cited : (46)

References (24)
  • 1
    • 0001626686 scopus 로고
    • Sur les equations linéaires aux différentielles ordinaires et aux différences finies
    • Poincaré H. Sur les equations linéaires aux différentielles ordinaires et aux différences finies. Amer. J. Math. 7:1885;203-258.
    • (1885) Amer. J. Math. , vol.7 , pp. 203-258
    • Poincaré, H.1
  • 2
    • 84934390415 scopus 로고
    • On the irregular cases of the linear ordinary difference equation
    • Adams C. R. On the irregular cases of the linear ordinary difference equation. Trans. Amer. Math. Soc. 30:1928;507-541.
    • (1928) Trans. Amer. Math. Soc. , vol.30 , pp. 507-541
    • Adams, C.R.1
  • 3
    • 51249192647 scopus 로고
    • Formal theory of irregular linear difference equations
    • Birkhoff G. D. Formal theory of irregular linear difference equations. Acta Math. 54:1930;205-246.
    • (1930) Acta Math. , vol.54 , pp. 205-246
    • Birkhoff, G.D.1
  • 4
    • 34250592508 scopus 로고
    • Analytic theory of singular difference equations
    • Birkhoff G. D., Trjitzinsky W. J. Analytic theory of singular difference equations. Acta Math. 60:1932;1-89.
    • (1932) Acta Math. , vol.60 , pp. 1-89
    • Birkhoff, G.D.1    Trjitzinsky, W.J.2
  • 5
    • 51249195000 scopus 로고
    • Analytic theory of linearq
    • Trjitzinsky W. J. Analytic theory of linearq. Acta Math. 61:1933;1-38.
    • (1933) Acta Math. , vol.61 , pp. 1-38
    • Trjitzinsky, W.J.1
  • 6
    • 0040571788 scopus 로고
    • Laplace integrals and factorial series in the theory of linear differential and linear difference equations
    • Trjitzinsky W. J. Laplace integrals and factorial series in the theory of linear differential and linear difference equations. Trans. Amer. Math. Soc. 37:1935;80-146.
    • (1935) Trans. Amer. Math. Soc. , vol.37 , pp. 80-146
    • Trjitzinsky, W.J.1
  • 7
    • 0011279580 scopus 로고
    • Convergent solutions of ordinary linear homogeneous difference equations
    • Culmer W. J. A., Harris W. A. Jr. Convergent solutions of ordinary linear homogeneous difference equations. Pacific J. Math. 13:1963;1111-1138.
    • (1963) Pacific J. Math. , vol.13 , pp. 1111-1138
    • Culmer, W.J.A.1    Harris W.A., Jr.2
  • 9
    • 0010516106 scopus 로고
    • Asymptotics of analytic difference equations
    • Berlin/New York: Springer-Verlag
    • Immink G. K. Asymptotics of analytic difference equations. Lecture Notes in Mathematics. 1984;Springer-Verlag, Berlin/New York.
    • (1984) Lecture Notes in Mathematics
    • Immink, G.K.1
  • 10
    • 0022133877 scopus 로고
    • Resurrecting the asymptotics of linear recurrences
    • Wimp J., Zeilberger D. Resurrecting the asymptotics of linear recurrences. J. Math. Anal. Appl. 111:1985;162-176.
    • (1985) J. Math. Anal. Appl. , vol.111 , pp. 162-176
    • Wimp, J.1    Zeilberger, D.2
  • 11
    • 0040622817 scopus 로고
    • Convergence properties of linear recurrence sequences
    • Kooman R. J., Tijdeman R. Convergence properties of linear recurrence sequences. Nieuw Arch. Wisk. (4). 4:1990;13-25.
    • (1990) Nieuw Arch. Wisk. (4) , vol.4 , pp. 13-25
    • Kooman, R.J.1    Tijdeman, R.2
  • 12
    • 0000278117 scopus 로고
    • Asymptotic Enumeration Methods
    • R.L. Graham, M. Grötschel, & L. Lovász. Amsterdam: Elsevier
    • Odlyzko A. M. Asymptotic Enumeration Methods. Graham R. L., Grötschel M., Lovász L. Handbook of Combinatorics. 1995;1130-1146 Elsevier, Amsterdam.
    • (1995) Handbook of Combinatorics , pp. 1130-1146
    • Odlyzko, A.M.1
  • 13
    • 0002293725 scopus 로고
    • Operator identities and the solution of linear matrix difference and differential equations
    • Verde-Star L. Operator identities and the solution of linear matrix difference and differential equations. Stud. Appl. Math. 91:1994;153-177.
    • (1994) Stud. Appl. Math. , vol.91 , pp. 153-177
    • Verde-Star, L.1
  • 18
    • 0039978965 scopus 로고
    • Explicit Methods of Solving Higher-Order Linear Differential Equations
    • New York: Wiley
    • Ross S. L. Explicit Methods of Solving Higher-Order Linear Differential Equations. Differential Equations. 1984;Wiley, New York.
    • (1984) Differential Equations
    • Ross, S.L.1
  • 20
    • 0031260784 scopus 로고    scopus 로고
    • On the solution of a second order linear homogeneous difference equation with variable coefficients
    • Mallik R. K. On the solution of a second order linear homogeneous difference equation with variable coefficients. J. Math. Anal. Appl. 215:1997;32-47.
    • (1997) J. Math. Anal. Appl. , vol.215 , pp. 32-47
    • Mallik, R.K.1
  • 21
    • 0039386731 scopus 로고
    • A representation of the solution of then
    • Kittappa R. K. A representation of the solution of then. Linear Algebra Appl. 193:1993;211-222.
    • (1993) Linear Algebra Appl. , vol.193 , pp. 211-222
    • Kittappa, R.K.1
  • 22
    • 0003171186 scopus 로고
    • Hypergeometric solutions of linear recurrences with polynomial coefficients
    • Petkovšek M. Hypergeometric solutions of linear recurrences with polynomial coefficients. J. Symbolic Comput. 14:1992;243-264.
    • (1992) J. Symbolic Comput. , vol.14 , pp. 243-264
    • Petkovšek, M.1
  • 23
    • 0039978963 scopus 로고
    • A generalization of Gosper's algorithm
    • Petkovšek M. A generalization of Gosper's algorithm. Discrete Math. 134:1994;125-131.
    • (1994) Discrete Math. , vol.134 , pp. 125-131
    • Petkovšek, M.1
  • 24
    • 21844524295 scopus 로고    scopus 로고
    • The combinatorial power of the companion matrix
    • Chen W. Y. C., Louck J. D. The combinatorial power of the companion matrix. Linear Algebra Appl. 232:1996;261-278.
    • (1996) Linear Algebra Appl. , vol.232 , pp. 261-278
    • Chen, W.Y.C.1    Louck, J.D.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.