A study of q -Laguerre polynomials through the T k , q , x -operator

Mumtaz Ahmad Khan

Czechoslovak Mathematical Journal (1997)

  • Volume: 47, Issue: 4, page 619-626
  • ISSN: 0011-4642

Abstract

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The present paper deals with certain generating functions and recurrence relations for q -Laguerre polynomials through the use of the T k , q , x -operator introduced in an earlier paper [7].

How to cite

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Khan, Mumtaz Ahmad. "A study of $q$-Laguerre polynomials through the $T_{k,q,x}$-operator." Czechoslovak Mathematical Journal 47.4 (1997): 619-626. <http://eudml.org/doc/30387>.

@article{Khan1997,
abstract = {The present paper deals with certain generating functions and recurrence relations for $q$-Laguerre polynomials through the use of the $T_\{k,q,x\}$-operator introduced in an earlier paper [7].},
author = {Khan, Mumtaz Ahmad},
journal = {Czechoslovak Mathematical Journal},
keywords = {Laguerre polynomials; generating functions; recurrence formulas},
language = {eng},
number = {4},
pages = {619-626},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A study of $q$-Laguerre polynomials through the $T_\{k,q,x\}$-operator},
url = {http://eudml.org/doc/30387},
volume = {47},
year = {1997},
}

TY - JOUR
AU - Khan, Mumtaz Ahmad
TI - A study of $q$-Laguerre polynomials through the $T_{k,q,x}$-operator
JO - Czechoslovak Mathematical Journal
PY - 1997
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 47
IS - 4
SP - 619
EP - 626
AB - The present paper deals with certain generating functions and recurrence relations for $q$-Laguerre polynomials through the use of the $T_{k,q,x}$-operator introduced in an earlier paper [7].
LA - eng
KW - Laguerre polynomials; generating functions; recurrence formulas
UR - http://eudml.org/doc/30387
ER -

References

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  1. Operational representation for the Laguerre and Hermite polynomials, Duke Math. Journal 31 (1964), 127–142. (1964) MR0159053
  2. 10.1002/mana.19650300105, Math. Nachr. 30 (1965), 47–61. (1965) MR0197804DOI10.1002/mana.19650300105
  3. 10.1002/mana.19490020604, Math. Nachr. 2 (1949), 340–379. (1949) MR0035344DOI10.1002/mana.19490020604
  4. Certain fractional q -integrals and q -derivatives, Nanta Mathematica 7 (1974), no. 1, 52–60. (1974) Zbl0289.33009MR0369630
  5. On q -Laguerre polynomials, Ganita 34 (1983), no. 1 and 2, 111–123. (1983) Zbl0638.33006MR0910619
  6. q -Analogue of certain operational formulae, Houston J. Math. 13 (1987), no. 1, pp. 75–82. (1987) MR0884235
  7. On a calculus for the T k , q , x -operator, Mathematica Balkanica, New series 6 (1992), fasc. 1, pp. 83–90. (1992) MR1170732
  8. On some operational representations of q -polynomials, Czechoslovak Mathematical Journal 45 (1995), 457–464. (1995) Zbl0836.33009MR1344511
  9. On some characterizations of q -Bessel polynomials, Acta Math. Viet. 15 (1990), no. 1, pp. 55–59. (1990) MR1087787
  10. Some generating functions, Univ. Lisbova Revista Fae. Ci A(2). Mat. 13 (1970), 43–51. (1970) Zbl0229.33015MR0308486
  11. Special Functions, The MacMillan Co., New York (1960). (1960) Zbl0092.06503MR0107725
  12. Generalized Hypergeometric Functions, Cambridge University Press (1966). (1966) Zbl0135.28101MR0201688
  13. A Treatise on Generating Functions, John Wiley and Sons (Halsted Press), New York, Ellis Horwood, Chichester, 1985. (1985) MR0750112

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