Dissertation/Thesis
Προβολή σε EDS

Some relations on Humbert matrix polynomials

Λεπτομέρειες βιβλιογραφικής εγγραφής
Τίτλος: Some relations on Humbert matrix polynomials
Συγγραφείς: Shehata, Ayman
Στοιχεία εκδότη: Institute of Mathematics, Academy of Sciences of the Czech Republic
Matematický ústav AV ČR
Έτος έκδοσης: 2016
Συλλογή: DML-CZ (Czech Digital Mathematics Library)
Θεματικοί όροι: keyword:hypergeometric matrix function, keyword:Humbert matrix polynomials, keyword:matrix functional calculus, keyword:generating matrix function, keyword:matrix differential equation, msc:15A60, msc:33C45, msc:33C55, msc:33E20
Περιγραφή: summary:The Humbert matrix polynomials were first studied by Khammash and Shehata (2012). Our goal is to derive some of their basic relations involving the Humbert matrix polynomials and then study several generating matrix functions, hypergeometric matrix representations, matrix differential equation and expansions in series of some relatively more familiar matrix polynomials of Legendre, Gegenbauer, Hermite, Laguerre and modified Laguerre. Finally, some definitions of generalized Humbert matrix polynomials also of two, three and several index are derived.
Τύπος εγγράφου: Thesis
Περιγραφή αρχείου: application/pdf
Γλώσσα: English
ISSN: 0862-7959
2464-7136
Relation: mr:MR3576790; zbl:Zbl 06674853; reference:[1] Aktaş, R.: A new multivariable extension of Humbert matrix polynomials.AIP Publishing LLC Rhodes, Greece AIP Conference Proceedings 1558: Proc. Int. Conf. on Numerical Analysis and Applied Mathematics (2013), 1128-1131 T. Simos et al. \DOI 10.1063/1.4825706. 10.1063/1.4825706; reference:[2] Aktaş, R.: A note on multivariable Humbert matrix polynomials.Gazi Univ. J. Sci. 27 (2014), 747-754.; reference:[3] Aktaş, R., Çekim, B., Çevik, A.: Extended Jacobi matrix polynomials.Util. Math. 92 (2013), 47-64. MR 3136666; reference:[4] Aktaş, R., Çekim, B., Şahin, R.: The matrix version for the multivariable Humbert polynomials.Miskolc Math. Notes 13 (2012), 197-208. Zbl 1274.33009, MR 3002623, 10.18514/MMN.2012.356; reference:[5] Altın, A., Çekim, B.: Generating matrix functions for Chebyshev matrix polynomials of the second kind.Hacet. J. Math. Stat. 41 (2012), 25-32. Zbl 1259.33014, MR 2976908; reference:[6] Altın, A., Çekim, B.: Some properties associated with Hermite matrix polynomials.Util. Math. 88 (2012), 171-181. Zbl 1262.15023, MR 2975830; reference:[7] Altın, A., Çekim, B.: Some miscellaneous properties for Gegenbauer matrix polynomials.Util. Math. 92 (2013), 377-387. Zbl 1293.33007, MR 3136694; reference:[8] Çekim, B., Altın, A., Aktaş, R.: Some relations satisfied by orthogonal matrix polynomials.Hacet. J. Math. Stat. 40 (2011), 241-253. Zbl 1229.33012, MR 2839191; reference:[9] Çekim, B., Altın, A., Aktaş, R.: Some new results for Jacobi matrix polynomials.Filomat 27 (2013), 713-719. MR 3243979, 10.2298/FIL1304713C; reference:[10] Defez, E., Jódar, L.: Some applications of the Hermite matrix polynomials series expansions.J. Comput. Appl. Math. 99 (1998), 105-117. Zbl 0929.33006, MR 1662687, 10.1016/S0377-0427(98)00149-6; reference:[11] Defez, E., Jódar, L.: Chebyshev matrix polynomials and second order matrix differential equations.Util. Math. 61 (2002), 107-123. Zbl 0998.15034, MR 1899321; reference:[12] Defez, E., Jódar, L., Law, A.: Jacobi matrix differential equation, polynomial solutions, and their properties.Comput. Math. Appl. 48 (2004), 789-803. Zbl 1069.33007, MR 2105252, 10.1016/j.camwa.2004.01.011; reference:[13] Dunford, N., Schwartz, J. T.: Linear Operators. Part I, General Theory.Pure and Applied Mathematics 7 A Wiley-Interscience Publishers, John Wiley & Sons, New York (1958). MR 1009162; reference:[14] James, A. T.: Special functions of matrix and single argument in statistics.Theory and Application of Special Functions, Proc. Advanced Sem., Math. Res. Center, Madison, Wis. R. A. Askey Academic Press, New York (1975), 497-520. Zbl 0326.33010, MR 0402145; reference:[15] Jódar, L., Company, R.: Hermite matrix polynomials and second order matrix differential equations.Approximation Theory Appl. 12 (1996), 20-30. MR 1465570; reference:[16] Jódar, L., Company, R., Ponsoda, E.: Orthogonal matrix polynomials and systems of second order differential equations.Differ. Equ. Dyn. Syst. 3 (1995), 269-288. Zbl 0892.33004, MR 1386749; reference:[17] Jódar, L., Cortés, J. C.: On the hypergeometric matrix function.J. Comput. Appl. Math. 99 (1998), 205-217. Zbl 0933.33004, MR 1662696, 10.1016/S0377-0427(98)00158-7; reference:[18] Jódar, L., Cortés, J. C.: Closed form general solution of the hypergeometric matrix differential equation.Math. Comput. Modelling 32 (2000), 1017-1028. Zbl 0985.33006, MR 1799616, 10.1016/S0895-7177(00)00187-4; reference:[19] Jódar, L., Defez, E.: On Hermite matrix polynomials and Hermite matrix functions.Approximation Theory Appl. 14 (1998), 36-48. MR 1651470; reference:[20] Jódar, L., Sastre, J.: On Laguerre matrix polynomials.Util. Math. 53 (1998), 37-48. Zbl 0990.33008, MR 1622055; reference:[21] Kargin, L., Kurt, V.: Some relations on Hermite matrix polynomials.Math. Comput. Appl. 18 (2013), 323-329. MR 3113139; reference:[22] Khammash, G. S., Shehata, A.: On Humbert matrix polynomials.Asian J. Current Eng. Maths. 1 (2012), 232-240 http://innovativejournal.in/index.php/ajcem/article/view/104/96.; reference:[23] Khan, S., Hassan, N. A. Makboul: 2-variable Laguerre matrix polynomials and Lie-algebraic techniques.J. Phys. A, Math. Theor. 43 (2010), Article ID 235204, 21 pages. MR 2646680, 10.1088/1751-8113/43/23/235204; reference:[24] Metwally, M. S., Mohamed, M. T., Shehata, A.: On Hermite-Hermite matrix polynomials.Math. Bohem. 133 (2008), 421-434. Zbl 1199.15079, MR 2472489; reference:[25] Sastre, J., Jódar, L.: On Laguerre matrix polynomial series.Util. Math. 71 (2006), 109-130. Zbl 1106.33011, MR 2278826; reference:[26] Shehata, A.: On Tricomi and Hermite-Tricomi matrix functions of complex variable.Commun. Math. Appl. 2 (2011), 97-109. Zbl 1266.33012, MR 3000027; reference:[27] Shehata, A.: A new extension of Gegenbauer matrix polynomials and their properties.Bull. Int. Math. Virtual Inst. 2 (2012), 29-42. MR 3149829; reference:[28] Shehata, A.: On pseudo Legendre matrix polynomials.Int. J. Math. Sci. Eng. Appl. 6 (2012), 251-258. MR 3057762; reference:[29] Shehata, A.: On Rainville's matrix polynomials.Sylwan J. 158 (2014), 158-178. MR 3248615; reference:[30] Shehata, A.: On Rice's matrix polynomials.Afr. Mat. 25 (2014), 757-777. Zbl 1321.15041, MR 3248615, 10.1007/s13370-013-0149-3; reference:[31] Shehata, A.: New kinds of hypergeometric matrix functions.British Journal of Mathematics and Computer Science 5 (2015), 92-102 \DOI 10.9734/BJMCS/2015/11492. 10.9734/BJMCS/2015/11492; reference:[32] Shehata, A.: On a new family of the extended generalized Bessel-type matrix polynomials.Mitteilungen Klosterneuburg J. 65 (2015), 100-121.; reference:[33] Shehata, A.: On modified Laguerre matrix polynomials.J. Nat. Sci. Math. 8 (2015), 153-166. MR 3404349; reference:[34] Taşdelen, F., Çekim, B., Aktaş, R.: On a multivariable extension of Jacobi matrix polynomials.Comput. Math. Appl. 61 (2011), 2412-2423. Zbl 1221.33022, MR 2794989, 10.1016/j.camwa.2011.02.019; reference:[35] Upadhyaya, L. M., Shehata, A.: On Legendre matrix polynomials and its applications.Int. Trans. Math. Sci. Comput. 4 (2011), 291-310. MR 3057762; reference:[36] Upadhyaya, L. M., Shehata, A.: A new extension of generalized Hermite matrix polynomials.Bull. Malays. Math. Sci. Soc. (2) 38 (2015), 165-179. Zbl 1311.33008, MR 3394046, 10.1007/s40840-014-0010-3; reference:[37] Varma, S., Çekim, B., Yeşildal, F. Taşdelen: On Konhauser matrix polynomials.Ars Comb. 100 (2011), 193-204. MR 2798172; reference:[38] Varma, S., Taşdelen, F.: Biorthogonal matrix polynomials related to Jacobi matrix polynomials.Comput. Math. Appl. 62 (2011), 3663-3668. Zbl 1236.15048, MR 2852088, 10.1016/j.camwa.2011.08.063
Διαθεσιμότητα: https://hdl.handle.net/10338.dmlcz/145954
Rights: access:Unrestricted ; rights:DML-CZ Czech Digital Mathematics Library, http://dml.cz/ ; rights:Institute of Mathematics AS CR, http://www.math.cas.cz/ ; conditionOfUse:http://dml.cz/use
Αριθμός Καταχώρησης: edsbas.95861131
Βάση Δεδομένων: BASE
FullText Text:
  Availability: 0
CustomLinks:
  – Url: https://hdl.handle.net/10338.dmlcz/145954#
    Name: EDS - BASE (ns324271)
    Category: fullText
    Text: View record from BASE
  – Url: https://resolver.ebsco.com/c/fiv2js/result?sid=EBSCO:edsbas&genre=article&issn=08627959&ISBN=&volume=&issue=&date=20160101&spage=&pages=&title=Some relations on Humbert matrix polynomials&atitle=Some%20relations%20on%20Humbert%20matrix%20polynomials&aulast=Shehata%2C%20Ayman&id=DOI:
    Name: Full Text Finder (for New FTF UI) (ns324271)
    Category: fullText
    Text: Full Text Finder
    MouseOverText: Full Text Finder
Header DbId: edsbas
DbLabel: BASE
An: edsbas.95861131
RelevancyScore: 709
AccessLevel: 3
PubType: Dissertation/Thesis
PubTypeId: unknown
PreciseRelevancyScore: 709.17822265625
IllustrationInfo
Items – Name: Title
  Label: Title
  Group: Ti
  Data: Some relations on Humbert matrix polynomials
– Name: Author
  Label: Authors
  Group: Au
  Data: <searchLink fieldCode="AR" term="%22Shehata%2C+Ayman%22">Shehata, Ayman</searchLink>
– Name: Publisher
  Label: Publisher Information
  Group: PubInfo
  Data: Institute of Mathematics, Academy of Sciences of the Czech Republic<br />Matematický ústav AV ČR
– Name: DatePubCY
  Label: Publication Year
  Group: Date
  Data: 2016
– Name: Subset
  Label: Collection
  Group: HoldingsInfo
  Data: DML-CZ (Czech Digital Mathematics Library)
– Name: Subject
  Label: Subject Terms
  Group: Su
  Data: <searchLink fieldCode="DE" term="%22keyword%3Ahypergeometric+matrix+function%22">keyword:hypergeometric matrix function</searchLink><br /><searchLink fieldCode="DE" term="%22keyword%3AHumbert+matrix+polynomials%22">keyword:Humbert matrix polynomials</searchLink><br /><searchLink fieldCode="DE" term="%22keyword%3Amatrix+functional+calculus%22">keyword:matrix functional calculus</searchLink><br /><searchLink fieldCode="DE" term="%22keyword%3Agenerating+matrix+function%22">keyword:generating matrix function</searchLink><br /><searchLink fieldCode="DE" term="%22keyword%3Amatrix+differential+equation%22">keyword:matrix differential equation</searchLink><br /><searchLink fieldCode="DE" term="%22msc%3A15A60%22">msc:15A60</searchLink><br /><searchLink fieldCode="DE" term="%22msc%3A33C45%22">msc:33C45</searchLink><br /><searchLink fieldCode="DE" term="%22msc%3A33C55%22">msc:33C55</searchLink><br /><searchLink fieldCode="DE" term="%22msc%3A33E20%22">msc:33E20</searchLink>
– Name: Abstract
  Label: Description
  Group: Ab
  Data: summary:The Humbert matrix polynomials were first studied by Khammash and Shehata (2012). Our goal is to derive some of their basic relations involving the Humbert matrix polynomials and then study several generating matrix functions, hypergeometric matrix representations, matrix differential equation and expansions in series of some relatively more familiar matrix polynomials of Legendre, Gegenbauer, Hermite, Laguerre and modified Laguerre. Finally, some definitions of generalized Humbert matrix polynomials also of two, three and several index are derived.
– Name: TypeDocument
  Label: Document Type
  Group: TypDoc
  Data: Thesis
– Name: Format
  Label: File Description
  Group: SrcInfo
  Data: application/pdf
– Name: Language
  Label: Language
  Group: Lang
  Data: English
– Name: ISSN
  Label: ISSN
  Group: ISSN
  Data: 0862-7959<br />2464-7136
– Name: NoteTitleSource
  Label: Relation
  Group: SrcInfo
  Data: mr:MR3576790; zbl:Zbl 06674853; reference:[1] Aktaş, R.: A new multivariable extension of Humbert matrix polynomials.AIP Publishing LLC Rhodes, Greece AIP Conference Proceedings 1558: Proc. Int. Conf. on Numerical Analysis and Applied Mathematics (2013), 1128-1131 T. Simos et al. \DOI 10.1063/1.4825706. 10.1063/1.4825706; reference:[2] Aktaş, R.: A note on multivariable Humbert matrix polynomials.Gazi Univ. J. Sci. 27 (2014), 747-754.; reference:[3] Aktaş, R., Çekim, B., Çevik, A.: Extended Jacobi matrix polynomials.Util. Math. 92 (2013), 47-64. MR 3136666; reference:[4] Aktaş, R., Çekim, B., Şahin, R.: The matrix version for the multivariable Humbert polynomials.Miskolc Math. Notes 13 (2012), 197-208. Zbl 1274.33009, MR 3002623, 10.18514/MMN.2012.356; reference:[5] Altın, A., Çekim, B.: Generating matrix functions for Chebyshev matrix polynomials of the second kind.Hacet. J. Math. Stat. 41 (2012), 25-32. Zbl 1259.33014, MR 2976908; reference:[6] Altın, A., Çekim, B.: Some properties associated with Hermite matrix polynomials.Util. Math. 88 (2012), 171-181. Zbl 1262.15023, MR 2975830; reference:[7] Altın, A., Çekim, B.: Some miscellaneous properties for Gegenbauer matrix polynomials.Util. Math. 92 (2013), 377-387. Zbl 1293.33007, MR 3136694; reference:[8] Çekim, B., Altın, A., Aktaş, R.: Some relations satisfied by orthogonal matrix polynomials.Hacet. J. Math. Stat. 40 (2011), 241-253. Zbl 1229.33012, MR 2839191; reference:[9] Çekim, B., Altın, A., Aktaş, R.: Some new results for Jacobi matrix polynomials.Filomat 27 (2013), 713-719. MR 3243979, 10.2298/FIL1304713C; reference:[10] Defez, E., Jódar, L.: Some applications of the Hermite matrix polynomials series expansions.J. Comput. Appl. Math. 99 (1998), 105-117. Zbl 0929.33006, MR 1662687, 10.1016/S0377-0427(98)00149-6; reference:[11] Defez, E., Jódar, L.: Chebyshev matrix polynomials and second order matrix differential equations.Util. Math. 61 (2002), 107-123. Zbl 0998.15034, MR 1899321; reference:[12] Defez, E., Jódar, L., Law, A.: Jacobi matrix differential equation, polynomial solutions, and their properties.Comput. Math. Appl. 48 (2004), 789-803. Zbl 1069.33007, MR 2105252, 10.1016/j.camwa.2004.01.011; reference:[13] Dunford, N., Schwartz, J. T.: Linear Operators. Part I, General Theory.Pure and Applied Mathematics 7 A Wiley-Interscience Publishers, John Wiley & Sons, New York (1958). MR 1009162; reference:[14] James, A. T.: Special functions of matrix and single argument in statistics.Theory and Application of Special Functions, Proc. Advanced Sem., Math. Res. Center, Madison, Wis. R. A. Askey Academic Press, New York (1975), 497-520. Zbl 0326.33010, MR 0402145; reference:[15] Jódar, L., Company, R.: Hermite matrix polynomials and second order matrix differential equations.Approximation Theory Appl. 12 (1996), 20-30. MR 1465570; reference:[16] Jódar, L., Company, R., Ponsoda, E.: Orthogonal matrix polynomials and systems of second order differential equations.Differ. Equ. Dyn. Syst. 3 (1995), 269-288. Zbl 0892.33004, MR 1386749; reference:[17] Jódar, L., Cortés, J. C.: On the hypergeometric matrix function.J. Comput. Appl. Math. 99 (1998), 205-217. Zbl 0933.33004, MR 1662696, 10.1016/S0377-0427(98)00158-7; reference:[18] Jódar, L., Cortés, J. C.: Closed form general solution of the hypergeometric matrix differential equation.Math. Comput. Modelling 32 (2000), 1017-1028. Zbl 0985.33006, MR 1799616, 10.1016/S0895-7177(00)00187-4; reference:[19] Jódar, L., Defez, E.: On Hermite matrix polynomials and Hermite matrix functions.Approximation Theory Appl. 14 (1998), 36-48. MR 1651470; reference:[20] Jódar, L., Sastre, J.: On Laguerre matrix polynomials.Util. Math. 53 (1998), 37-48. Zbl 0990.33008, MR 1622055; reference:[21] Kargin, L., Kurt, V.: Some relations on Hermite matrix polynomials.Math. Comput. Appl. 18 (2013), 323-329. MR 3113139; reference:[22] Khammash, G. S., Shehata, A.: On Humbert matrix polynomials.Asian J. Current Eng. Maths. 1 (2012), 232-240 http://innovativejournal.in/index.php/ajcem/article/view/104/96.; reference:[23] Khan, S., Hassan, N. A. Makboul: 2-variable Laguerre matrix polynomials and Lie-algebraic techniques.J. Phys. A, Math. Theor. 43 (2010), Article ID 235204, 21 pages. MR 2646680, 10.1088/1751-8113/43/23/235204; reference:[24] Metwally, M. S., Mohamed, M. T., Shehata, A.: On Hermite-Hermite matrix polynomials.Math. Bohem. 133 (2008), 421-434. Zbl 1199.15079, MR 2472489; reference:[25] Sastre, J., Jódar, L.: On Laguerre matrix polynomial series.Util. Math. 71 (2006), 109-130. Zbl 1106.33011, MR 2278826; reference:[26] Shehata, A.: On Tricomi and Hermite-Tricomi matrix functions of complex variable.Commun. Math. Appl. 2 (2011), 97-109. Zbl 1266.33012, MR 3000027; reference:[27] Shehata, A.: A new extension of Gegenbauer matrix polynomials and their properties.Bull. Int. Math. Virtual Inst. 2 (2012), 29-42. MR 3149829; reference:[28] Shehata, A.: On pseudo Legendre matrix polynomials.Int. J. Math. Sci. Eng. Appl. 6 (2012), 251-258. MR 3057762; reference:[29] Shehata, A.: On Rainville's matrix polynomials.Sylwan J. 158 (2014), 158-178. MR 3248615; reference:[30] Shehata, A.: On Rice's matrix polynomials.Afr. Mat. 25 (2014), 757-777. Zbl 1321.15041, MR 3248615, 10.1007/s13370-013-0149-3; reference:[31] Shehata, A.: New kinds of hypergeometric matrix functions.British Journal of Mathematics and Computer Science 5 (2015), 92-102 \DOI 10.9734/BJMCS/2015/11492. 10.9734/BJMCS/2015/11492; reference:[32] Shehata, A.: On a new family of the extended generalized Bessel-type matrix polynomials.Mitteilungen Klosterneuburg J. 65 (2015), 100-121.; reference:[33] Shehata, A.: On modified Laguerre matrix polynomials.J. Nat. Sci. Math. 8 (2015), 153-166. MR 3404349; reference:[34] Taşdelen, F., Çekim, B., Aktaş, R.: On a multivariable extension of Jacobi matrix polynomials.Comput. Math. Appl. 61 (2011), 2412-2423. Zbl 1221.33022, MR 2794989, 10.1016/j.camwa.2011.02.019; reference:[35] Upadhyaya, L. M., Shehata, A.: On Legendre matrix polynomials and its applications.Int. Trans. Math. Sci. Comput. 4 (2011), 291-310. MR 3057762; reference:[36] Upadhyaya, L. M., Shehata, A.: A new extension of generalized Hermite matrix polynomials.Bull. Malays. Math. Sci. Soc. (2) 38 (2015), 165-179. Zbl 1311.33008, MR 3394046, 10.1007/s40840-014-0010-3; reference:[37] Varma, S., Çekim, B., Yeşildal, F. Taşdelen: On Konhauser matrix polynomials.Ars Comb. 100 (2011), 193-204. MR 2798172; reference:[38] Varma, S., Taşdelen, F.: Biorthogonal matrix polynomials related to Jacobi matrix polynomials.Comput. Math. Appl. 62 (2011), 3663-3668. Zbl 1236.15048, MR 2852088, 10.1016/j.camwa.2011.08.063
– Name: URL
  Label: Availability
  Group: URL
  Data: https://hdl.handle.net/10338.dmlcz/145954
– Name: Copyright
  Label: Rights
  Group: Cpyrght
  Data: access:Unrestricted ; rights:DML-CZ Czech Digital Mathematics Library, http://dml.cz/ ; rights:Institute of Mathematics AS CR, http://www.math.cas.cz/ ; conditionOfUse:http://dml.cz/use
– Name: AN
  Label: Accession Number
  Group: ID
  Data: edsbas.95861131
PLink https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsbas&AN=edsbas.95861131
RecordInfo BibRecord:
  BibEntity:
    Languages:
      – Text: English
    Subjects:
      – SubjectFull: keyword:hypergeometric matrix function
        Type: general
      – SubjectFull: keyword:Humbert matrix polynomials
        Type: general
      – SubjectFull: keyword:matrix functional calculus
        Type: general
      – SubjectFull: keyword:generating matrix function
        Type: general
      – SubjectFull: keyword:matrix differential equation
        Type: general
      – SubjectFull: msc:15A60
        Type: general
      – SubjectFull: msc:33C45
        Type: general
      – SubjectFull: msc:33C55
        Type: general
      – SubjectFull: msc:33E20
        Type: general
    Titles:
      – TitleFull: Some relations on Humbert matrix polynomials
        Type: main
  BibRelationships:
    HasContributorRelationships:
      – PersonEntity:
          Name:
            NameFull: Shehata, Ayman
    IsPartOfRelationships:
      – BibEntity:
          Dates:
            – D: 01
              M: 01
              Type: published
              Y: 2016
          Identifiers:
            – Type: issn-print
              Value: 08627959
            – Type: issn-print
              Value: 24647136
            – Type: issn-locals
              Value: edsbas
ResultId 1