메뉴 건너뛰기




Volumn 11, Issue 2, 2006, Pages 139-158

Padé approximations to the logarithm II: Identities, recurrences, and symbolic computation

Author keywords

Combinatorial identities; Computer algebra; Creative telescoping; Pad approximation

Indexed keywords


EID: 33744718824     PISSN: 13824090     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11139-006-6503-4     Document Type: Article
Times cited : (14)

References (27)
  • 1
    • 85031698900 scopus 로고
    • D'Alembertian solutions of linear differential and difference equations
    • Gathen, J.von zur, (ed.). ACM Press, Baltimore
    • Abramov, S.A., Petkovšek, M.: D'Alembertian solutions of linear differential and difference equations. In: Gathen, J.von zur, (ed.), Proc. ISSAC'94, pp. 169-174. ACM Press, Baltimore (1994)
    • (1994) Proc. ISSAC'94 , pp. 169-174
    • Abramov, S.A.1    Petkovšek, M.2
  • 2
    • 25444477561 scopus 로고
    • Quadratic and higher order Padé approximants
    • Budapest
    • Borwein, P.B.: Quadratic and higher order Padé approximants. In: A. Haar memorial conference, Vol. I, II(Budapest, 1985)
    • (1985) A. Haar Memorial Conference , vol.1-2
    • Borwein, P.B.1
  • 3
    • 33744722743 scopus 로고
    • North-Holland, Amsterdam
    • volume 49 of Colloq. Math. Soc. János Bolyai, North-Holland, Amsterdam, pp. 213-224 (1987)
    • (1987) Colloq. Math. Soc. János Bolyai , vol.49 , pp. 213-224
  • 4
    • 0041684683 scopus 로고    scopus 로고
    • On solutions of linear ordinary difference equations in their coefficient field
    • Bronstein, M.: On solutions of linear ordinary difference equations in their coefficient field. J. Symbolic Comput. 29(6), 841-877 (2000)
    • (2000) J. Symbolic Comput. , vol.29 , Issue.6 , pp. 841-877
    • Bronstein, M.1
  • 5
    • 0004107349 scopus 로고
    • Interscience Publishers, John Wiley & Sons
    • Cohn, R.M.: Difference algebra. Interscience Publishers, John Wiley & Sons (1965)
    • (1965) Difference Algebra
    • Cohn, R.M.1
  • 6
    • 33751501378 scopus 로고    scopus 로고
    • Padé approximations to the logarithm III: Alternative methods and additional results
    • to appear
    • Driver, K., Prodinger, H., Schneider, C., Weideman, J.A.C.: Padé approximations to the logarithm III: Alternative methods and additional results. Ramanujan J., to appear
    • Ramanujan J.
    • Driver, K.1    Prodinger, H.2    Schneider, C.3    Weideman, J.A.C.4
  • 7
    • 0038840100 scopus 로고
    • Decision procedures for indefinite hypergeometric summation
    • Gosper, R.W.: Decision procedures for indefinite hypergeometric summation. Proc. Nat. Acad. Sci. U.S.A. 75, 40-42 (1978)
    • (1978) Proc. Nat. Acad. Sci. U.S.A. , vol.75 , pp. 40-42
    • Gosper, R.W.1
  • 9
    • 0033092922 scopus 로고    scopus 로고
    • Solving difference equations in finite terms
    • Hendriks, P.A., Singer, M.F.: Solving difference equations in finite terms. J. Symbolic Comput. 27(3), 239-259, (1999)
    • (1999) J. Symbolic Comput. , vol.27 , Issue.3 , pp. 239-259
    • Hendriks, P.A.1    Singer, M.F.2
  • 11
    • 84976849768 scopus 로고
    • Summation in finite terms
    • Karr, M.: Summation in finite terms. J. ACM 28, 305-350 (1981)
    • (1981) J. ACM , vol.28 , pp. 305-350
    • Karr, M.1
  • 12
    • 84984634412 scopus 로고
    • Theory of summation in finite terms
    • Karr, M.: Theory of summation in finite terms. J. Symbolic Comput. 1, 303-315 (1985)
    • (1985) J. Symbolic Comput. , vol.1 , pp. 303-315
    • Karr, M.1
  • 13
    • 0001487910 scopus 로고    scopus 로고
    • A mathematica q-analogue of Zeilberger's algorithm based on an algebraically motivated aproach to q-hypergeometric telescoping
    • Ismail, M. and Rahman, M., (eds.) Fields Institute Toronto. AMS
    • Paule, P., Riese, A.: A mathematica q-analogue of Zeilberger's algorithm based on an algebraically motivated aproach to q-hypergeometric telescoping. In: Ismail, M. and Rahman, M., (eds.) Special Functions, q-Series and Related Topics, volume 14, Fields Institute Toronto, pp. 179-210. AMS (1997)
    • (1997) Special Functions, Q-series and Related Topics , vol.14 , pp. 179-210
    • Paule, P.1    Riese, A.2
  • 14
    • 0141838153 scopus 로고    scopus 로고
    • Computer proofs of a new family of harmonic number identities
    • Paule, P., Schneider, C.: Computer proofs of a new family of harmonic number identities. Adv. in Appl. Math. 31(2), 359-378 (2003)
    • (2003) Adv. in Appl. Math. , vol.31 , Issue.2 , pp. 359-378
    • Paule, P.1    Schneider, C.2
  • 15
    • 0000210471 scopus 로고
    • A Mathematica version of Zeilberger's algorithm for proving binomial coefficient identities
    • Paule, P., Schorn, M.: A Mathematica version of Zeilberger's algorithm for proving binomial coefficient identities. J. Symbolic Comput. 20(5-6), 673-698 (1995)
    • (1995) J. Symbolic Comput. , vol.20 , Issue.5-6 , pp. 673-698
    • Paule, P.1    Schorn, M.2
  • 18
    • 84966223571 scopus 로고
    • The solution to the problem of integration in finite terms
    • Risch, R.: The solution to the problem of integration in finite terms. Bull. Amer. Math. Soc. 76, 605-608 (1970)
    • (1970) Bull. Amer. Math. Soc. , vol.76 , pp. 605-608
    • Risch, R.1
  • 19
    • 15844368051 scopus 로고    scopus 로고
    • The summation package Sigma: Underlying principles and a rhombus tiling application
    • Schneider, C.: The summation package Sigma: Underlying principles and a rhombus tiling application. Discrete Math. Theor. Comput. Sci. 6(2), 365-386 (2004)
    • (2004) Discrete Math. Theor. Comput. Sci. , vol.6 , Issue.2 , pp. 365-386
    • Schneider, C.1
  • 20
    • 0141480367 scopus 로고    scopus 로고
    • Symbolic summation in difference fields
    • RISC-Linz, J. Kepler University. PhD Thesis
    • Schneider, C.: Symbolic summation in difference fields. Technical Report 01-17, RISC-Linz, J. Kepler University. PhD Thesis (2001)
    • (2001) Technical Report , vol.1 , Issue.17
    • Schneider, C.1
  • 21
    • 15844414168 scopus 로고    scopus 로고
    • Degree bounds to find polynomial solutions of parameterized linear difference equations in Π∑-fields
    • Schneider, C.: Degree bounds to find polynomial solutions of parameterized linear difference equations in Π∑-fields. Appl. Algebra. Engrg. Comm. Comput. 16(1), 1-32 (2005)
    • (2005) Appl. Algebra. Engrg. Comm. Comput. , vol.16 , Issue.1 , pp. 1-32
    • Schneider, C.1
  • 22
    • 15844417223 scopus 로고    scopus 로고
    • A collection of denominator bounds to solve parameterized linear difference equations in Π∑-extensions
    • Petcu, D. et al. (eds.). Milton Publishing
    • Schneider, C.: A collection of denominator bounds to solve parameterized linear difference equations in Π∑-extensions. In: Petcu, D. et al. (eds.) Proc. SYNASC04, 6th Internat. Symposium on Symbolic and Numeric Algorithms for Scientfic Computation, pp. 269-282. Milton Publishing (2004)
    • (2004) Proc. SYNASC04, 6th Internat. Symposium on Symbolic and Numeric Algorithms for Scientfic Computation , pp. 269-282
    • Schneider, C.1
  • 23
    • 24344486864 scopus 로고    scopus 로고
    • Solving parameterized linear difference equations in terms of indefinite nested sums and products
    • Schneider, C.: Solving parameterized linear difference equations in terms of indefinite nested sums and products. J. Differ. Equations Appl. 11(9), 799-821 (2005)
    • (2005) J. Differ. Equations Appl. , vol.11 , Issue.9 , pp. 799-821
    • Schneider, C.1
  • 24
    • 33749560321 scopus 로고    scopus 로고
    • Finding telescopers with minimal depth for indefinite nested sum and product expressions
    • Kauers, M. (ed.). ACM
    • Schneider, C.: Finding telescopers with minimal depth for indefinite nested sum and product expressions. In: Kauers, M. (ed.) Proc. ISSAC'05, pp. 285-292. ACM (2005)
    • (2005) Proc. ISSAC'05 , pp. 285-292
    • Schneider, C.1
  • 25
  • 26
    • 25444450270 scopus 로고    scopus 로고
    • Padé approximations to the logarithm I: Derivation via differential equations
    • Weideman, J.A.C.: Padé approximations to the logarithm I: Derivation via differential equations. Quaest. Math. 28(3), 375-390 (2005)
    • (2005) Quaest. Math. , vol.28 , Issue.3 , pp. 375-390
    • Weideman, J.A.C.1
  • 27
    • 0002128111 scopus 로고
    • A fast algorithm for proving terminating hypergeometric identities
    • Zeilberger, D.: A fast algorithm for proving terminating hypergeometric identities. Discrete Math. 80(2), 207-211 (1990)
    • (1990) Discrete Math. , vol.80 , Issue.2 , pp. 207-211
    • Zeilberger, D.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.