-
1
-
-
0002803522
-
Characterization theorems for orthogonal polynomials, Orthogonal polynomials
-
Columbus, OH Kluwer Acad. Publ., Dordrecht
-
W.A. Al-Salam, Characterization theorems for orthogonal polynomials, in: Orthogonal polynomials (Columbus, OH, 1989), vol. 294 of NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., Kluwer Acad. Publ., Dordrecht, 1990, pp. 1-24.
-
(1989)
NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci.
, vol.294
, pp. 1-24
-
-
Al-Salam, W.A.1
-
2
-
-
33745891556
-
On characterizations of classical polynomials
-
R. Álvarez Nodarse On characterizations of classical polynomials J. Comput. Appl. Math. 196 1 2006 320 337
-
(2006)
J. Comput. Appl. Math.
, vol.196
, Issue.1
, pp. 320-337
-
-
Álvarez Nodarse, R.1
-
3
-
-
0001683859
-
Classical orthogonal polynomials, Orthogonal polynomials and applications (Bar-le-Duc, 1984)
-
Springer, Berlin
-
G.E. Andrews, R. Askey, Classical orthogonal polynomials, in: Orthogonal polynomials and applications (Bar-le-Duc, 1984), vol. 1171 of Lecture Notes in Math., Springer, Berlin, 1985, pp. 36-62.
-
(1985)
Lecture Notes in Math.
, vol.1171
, pp. 36-62
-
-
Andrews, G.E.1
Askey, R.2
-
4
-
-
84871602570
-
On limit relations between some families of bivariate hypergeometric orthogonal polynomials
-
035202
-
I. Area, E. Godoy, On limit relations between some families of bivariate hypergeometric orthogonal polynomials, J. Phys. A: Math. Theor. 46 (035202) (2013) 11 pp.
-
(2013)
J. Phys. A: Math. Theor
, vol.46
, pp. 11
-
-
Area, I.1
Godoy, E.2
-
5
-
-
84855826207
-
On a class of bivariate second-order linear partial difference equations and their monic orthogonal polynomial solutions
-
I. Area, E. Godoy, and J. Rodal On a class of bivariate second-order linear partial difference equations and their monic orthogonal polynomial solutions J. Math. Anal. Appl. 389 2012 165 178
-
(2012)
J. Math. Anal. Appl.
, vol.389
, pp. 165-178
-
-
Area, I.1
Godoy, E.2
Rodal, J.3
-
6
-
-
80255138716
-
Bivariate second-order linear partial differential equations and orthogonal polynomial solutions
-
I. Area, E. Godoy, A. Ronveaux, and A. Zarzo Bivariate second-order linear partial differential equations and orthogonal polynomial solutions J. Math. Anal. Appl. 387 2 2012 1188 1208
-
(2012)
J. Math. Anal. Appl.
, vol.387
, Issue.2
, pp. 1188-1208
-
-
Area, I.1
Godoy, E.2
Ronveaux, A.3
Zarzo, A.4
-
7
-
-
0001308382
-
Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials
-
iv+55
-
R. Askey, J. Wilson, Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials, Mem. Amer. Math. Soc. 54 (319) (1985) iv+55.
-
(1985)
Mem. Amer. Math. Soc
, vol.54
, Issue.319
-
-
Askey, R.1
Wilson, J.2
-
9
-
-
0000032737
-
Über sturm-liouvillesche polynomsysteme
-
S. Bochner Über Sturm-Liouvillesche Polynomsysteme Math. Z. 29 1 1929 730 736
-
(1929)
Math. Z.
, vol.29
, Issue.1
, pp. 730-736
-
-
Bochner, S.1
-
10
-
-
0006340277
-
On polynomial solutions of a class of linear differential equations of the second order
-
W.C. Brenke On polynomial solutions of a class of linear differential equations of the second order Bull. Amer. Math. Soc. 36 2 1930 77 84
-
(1930)
Bull. Amer. Math. Soc.
, vol.36
, Issue.2
, pp. 77-84
-
-
Brenke, W.C.1
-
11
-
-
0003362637
-
An introduction to orthogonal polynomials
-
Gordon and Breach Science Publishers, New York
-
T.S. Chihara, An introduction to orthogonal polynomials, in: Mathematics and its Applications, vol. 13, Gordon and Breach Science Publishers, New York, 1978.
-
(1978)
Mathematics and Its Applications
, vol.13
-
-
Chihara, T.S.1
-
12
-
-
0003358801
-
Rodrigues' formula and the classical orthogonal polynomials
-
C.W. Cryer, Rodrigues' formula and the classical orthogonal polynomials, Boll. Un. Mat. Ital. (4) 3 (1970) 1-11.
-
(1970)
Boll. Un. Mat. Ital
, vol.3
, Issue.4
, pp. 1-11
-
-
Cryer, C.W.1
-
13
-
-
84952652748
-
Orthogonal polynomials of several variables
-
Cambridge University Press, Cambridge
-
C.F. Dunkl, Y. Xu, Orthogonal polynomials of several variables, vol. 81 of Encyclopedia of Mathematics and its Applications, Cambridge University Press, Cambridge, 2001.
-
(2001)
Encyclopedia of Mathematics and Its Applications
, vol.81
-
-
Dunkl, C.F.1
Xu, Y.2
-
14
-
-
33746682231
-
Basic hypergeometric series
-
96 second ed Cambridge University Press, Cambridge
-
G. Gasper, M. Rahman, Basic hypergeometric series, vol. 96 of Encyclopedia of Mathematics and its Applications, second ed., Cambridge University Press, Cambridge, 2004.
-
(2004)
Encyclopedia of Mathematics and Its Applications
-
-
Gasper, G.1
Rahman, M.2
-
15
-
-
84884759681
-
Q-Analogues of some multivariable biorthogonal polynomials
-
Dev. Math., Springer, New York
-
G. Gasper, M. Rahman, q-Analogues of some multivariable biorthogonal polynomials, in: Theory and applications of special functions, vol. 13 of Dev. Math., Springer, New York, 2005, pp. 185-208.
-
(2005)
Theory and Applications of Special Functions
, vol.13
, pp. 185-208
-
-
Gasper, G.1
Rahman, M.2
-
16
-
-
33845756995
-
Some systems of multivariable orthogonal Askey-Wilson polynomials
-
Dev. Math., Springer, New York
-
G. Gasper, M. Rahman, Some systems of multivariable orthogonal Askey-Wilson polynomials, in: Theory and applications of special functions, vol. 13 of Dev. Math., Springer, New York, 2005, pp. 209-219.
-
(2005)
Theory and Applications of Special Functions
, vol.13
, pp. 209-219
-
-
Gasper, G.1
Rahman, M.2
-
17
-
-
33845732591
-
Some systems of multivariable orthogonal q-Racah polynomials
-
G. Gasper, and M. Rahman Some systems of multivariable orthogonal q-Racah polynomials Ramanujan J. 13 1-3 2007 389 405
-
(2007)
Ramanujan J.
, vol.13
, Issue.13
, pp. 389-405
-
-
Gasper, G.1
Rahman, M.2
-
18
-
-
77955087374
-
Bispectrality of multivariable Racah-Wilson polynomials
-
J.S. Geronimo, and P. Iliev Bispectrality of multivariable Racah-Wilson polynomials Constr. Approx. 31 3 2010 417 457
-
(2010)
Constr. Approx.
, vol.31
, Issue.3
, pp. 417-457
-
-
Geronimo, J.S.1
Iliev, P.2
-
19
-
-
79953044603
-
Multivariable Askey-Wilson function and bispectrality
-
J.S. Geronimo, and P. Iliev Multivariable Askey-Wilson function and bispectrality Ramanujan J. 24 3 2011 273 287
-
(2011)
Ramanujan J.
, vol.24
, Issue.3
, pp. 273-287
-
-
Geronimo, J.S.1
Iliev, P.2
-
20
-
-
0003124908
-
Über Orthogonalpolynome, die q-Differenzengleichungen genügen
-
W. Hahn Über Orthogonalpolynome, die q-Differenzengleichungen genügen Math. Nachr. 2 1949 4 34
-
(1949)
Math. Nachr.
, vol.2
, pp. 4-34
-
-
Hahn, W.1
-
21
-
-
0000335910
-
Root systems and hypergeometric functions. i
-
G.J. Heckman, and E.M. Opdam Root systems and hypergeometric functions. I Compositio Math. 64 3 1987 329 352
-
(1987)
Compositio Math.
, vol.64
, Issue.3
, pp. 329-352
-
-
Heckman, G.J.1
Opdam, E.M.2
-
22
-
-
84871593305
-
Sur un nouveau développement en série de functions
-
Paris (Reprinted in Hermite, C. Oeuvres complétes Paris 93-100 and 266-273
-
C. Hermite, Sur un nouveau développement en série de fonctions, Compt. Rend. Acad. Sci. Paris (Reprinted in Hermite, C. Oeuvres complétes, vol. 2, 1908, Paris, pp. 293-308.) 58 (1864) 93-100 and 266-273.
-
(1908)
Compt Rend. Acad. Sci
, vol.2
, Issue.1864
, pp. 293-308
-
-
Hermite, C.1
-
23
-
-
33644949358
-
Classical and quantum orthogonal polynomials in one variable
-
Cambridge University Press, Cambridge
-
M.E.H. Ismail, Classical and quantum orthogonal polynomials in one variable, vol. 98 of Encyclopedia of Mathematics and its Applications, Cambridge University Press, Cambridge, 2005.
-
(2005)
Encyclopedia of Mathematics and Its Applications
, vol.98
-
-
Ismail, M.E.H.1
-
24
-
-
0001483988
-
On q-definite integrals, Q.J
-
F. Jackson On q-definite integrals, Q.J Pure Appl. Math. 41 1910 193 203
-
(1910)
Pure Appl. Math.
, vol.41
, pp. 193-203
-
-
Jackson, F.1
-
25
-
-
14844360640
-
Rodrigues type formula for multi-variate orthogonal polynomials
-
Y.J. Kim, K.H. Kwon, and J.K. Lee Rodrigues type formula for multi-variate orthogonal polynomials Bull. Korean Math. Soc. 38 3 2001 463 474
-
(2001)
Bull. Korean Math. Soc.
, vol.38
, Issue.3
, pp. 463-474
-
-
Kim, Y.J.1
Kwon, K.H.2
Lee, J.K.3
-
27
-
-
0000515270
-
Askey-Wilson polynomials for root systems of type BC
-
(Tampa, FL, 1991) Contemp. Math., Amer. Math. Soc., Providence, RI
-
T.H. Koornwinder, Askey-Wilson polynomials for root systems of type BC, in: Hypergeometric functions on domains of positivity, Jack polynomials, and applications (Tampa, FL, 1991), vol. 138 of Contemp. Math., Amer. Math. Soc., Providence, RI, 1992, pp. 189-204.
-
(1992)
Hypergeometric Functions on Domains of Positivity, Jack Polynomials, and Applications
, vol.138
, pp. 189-204
-
-
Koornwinder, T.H.1
-
28
-
-
0001939979
-
Compact quantum groups and q-special functions
-
Representations of Lie groups and quantum groups (Trento, 1993) Longman Sci. Tech., Harlow
-
T.H. Koornwinder, Compact quantum groups and q-special functions, in: Representations of Lie groups and quantum groups (Trento, 1993), vol. 311 of Pitman Res. Notes Math. Ser., Longman Sci. Tech., Harlow, 1994, pp. 46-128.
-
(1994)
Pitman Res. Notes Math. Ser.
, vol.311
, pp. 46-128
-
-
Koornwinder, T.H.1
-
29
-
-
34547107360
-
The structure relation for Askey-Wilson polynomials
-
DOI 10.1016/j.cam.2006.10.015, PII S0377042706006029
-
T.H. Koornwinder The structure relation for Askey-Wilson polynomials J. Comput. Appl. Math. 207 2 2007 214 226 (Pubitemid 47102001)
-
(2007)
Journal of Computational and Applied Mathematics
, vol.207
, Issue.2
, pp. 214-226
-
-
Koornwinder, T.H.1
-
30
-
-
0000105784
-
Orthogonality and recursion formulas for polynomials in nvariables
-
M.A. Kowalski Orthogonality and recursion formulas for polynomials in nvariables SIAM J. Math. Anal. 13 2 1982 316 323
-
(1982)
SIAM J. Math. Anal.
, vol.13
, Issue.2
, pp. 316-323
-
-
Kowalski, M.A.1
-
31
-
-
0008909251
-
The recursion formulas for orthogonal polynomials in nvariables
-
M.A. Kowalski The recursion formulas for orthogonal polynomials in nvariables SIAM J. Math. Anal. 13 2 1982 309 315
-
(1982)
SIAM J. Math. Anal.
, vol.13
, Issue.2
, pp. 309-315
-
-
Kowalski, M.A.1
-
32
-
-
0000188322
-
Orthogonal polynomials in two variables
-
H.L. Krall, I.M. Sheffer, Orthogonal polynomials in two variables, Ann. Mat. Pura Appl. (4) 76 (1967) 325-376.
-
(1967)
Ann. Mat. Pura Appl
, vol.76
, Issue.4
, pp. 325-376
-
-
Krall, H.L.1
Sheffer, I.M.2
-
33
-
-
0003876952
-
Orthogonal polynomials and applications (Bar-le-Duc, 1984)
-
Springer, Berlin
-
J. Labelle, Tableau d'Askey, in: Orthogonal polynomials and applications (Bar-le-Duc, 1984), vol. 1171 of Lecture Notes in Math., Springer, Berlin, 1985, pp. xxxvi-xxxvii.
-
(1985)
Lecture Notes in Math.
, vol.1171
-
-
Labelle, J.1
D'Askey, T.2
-
34
-
-
80051548478
-
Two-variable orthogonal polynomials of big q-Jacobi type
-
S. Lewanowicz, and P. Woźny Two-variable orthogonal polynomials of big q-Jacobi type J. Comput. Appl. Math. 233 6 2010 1554 1561
-
(2010)
J. Comput. Appl. Math.
, vol.233
, Issue.6
, pp. 1554-1561
-
-
Lewanowicz, S.1
Woźny, P.2
-
35
-
-
84876110119
-
Structure relations for the bivariate big q-Jacobi polynomials
-
S. Lewanowicz, P. Woźny, and R. Nowak Structure relations for the bivariate big q-Jacobi polynomials Appl. Math. Comput. 219 16 2013 8790 8802
-
(2013)
Appl. Math. Comput.
, vol.219
, Issue.16
, pp. 8790-8802
-
-
Lewanowicz, S.1
Woźny, P.2
Nowak, R.3
-
36
-
-
0041892041
-
Orthogonal polynomials in several variables
-
A. Lyskova, Orthogonal polynomials in several variables., Sov. Math., Dokl. 43 (1) (1991) 264-268.
-
(1991)
Sov. Math., Dokl.
, vol.43
, Issue.1
, pp. 264-268
-
-
Lyskova, A.1
-
37
-
-
0003267686
-
Symmetric functions and Hall polynomials
-
second ed., The Clarendon Press Oxford University Press, New York Oxford Science Publications
-
I.G. Macdonald, Symmetric functions and Hall polynomials, Oxford Mathematical Monographs, second ed., The Clarendon Press Oxford University Press, New York, 1995. Oxford Science Publications.
-
(1995)
Oxford Mathematical Monographs
-
-
Macdonald, I.G.1
-
38
-
-
53049103411
-
Simultaneous determination of ternary drug mixtures using square wave polarography subjected to non-parametric and chemometric peak convolution
-
H.M. Maher, and R.M. Youssef Simultaneous determination of ternary drug mixtures using square wave polarography subjected to non-parametric and chemometric peak convolution Chemometr. Intell. Lab. Syst. 94 2 2008 95 103
-
(2008)
Chemometr. Intell. Lab. Syst.
, vol.94
, Issue.2
, pp. 95-103
-
-
Maher, H.M.1
Youssef, R.M.2
-
42
-
-
84884770632
-
-
N.I. of Standards, Technology, Digital library of mathematical functions, Release date 2012-03-23
-
N.I. of Standards, Technology, Digital library of mathematical functions, http://dlmf.nist.gov/ Release date 2012-03-23
-
-
-
-
43
-
-
84876159902
-
-
Ph.D. thesis, Departamento de Matemática Aplicada II Universidade de Vigo, Vigo
-
J. Rodal, Polinomios ortogonales en varias variables discretas, Ph.D. thesis, Departamento de Matemática Aplicada II, Universidade de Vigo, Vigo, 2008.
-
(2008)
Polinomios Ortogonales en Varias Variables Discretas
-
-
Rodal, J.1
-
44
-
-
27844596662
-
Orthogonal polynomials of two discrete variables on the simplex
-
DOI 10.1080/1065246042000272036
-
J. Rodal, I. Area, and E. Godoy Orthogonal polynomials of two discrete variables on the simplex Integr. Transf. Spec. Funct. 16 3 2005 263 280 (Pubitemid 41657245)
-
(2005)
Integral Transforms and Special Functions
, vol.16
, Issue.3
, pp. 263-280
-
-
Rodal, J.1
Area, I.2
Godoy, E.3
-
45
-
-
33846062380
-
Linear partial difference equations of hypergeometric type: Orthogonal polynomial solutions in two discrete variables
-
DOI 10.1016/j.cam.2006.01.027, PII S0377042706000690
-
J. Rodal, I. Area, and E. Godoy Linear partial difference equations of hypergeometric type: orthogonal polynomial solutions in two discrete variables J. Comput. Appl. Math. 200 2 2007 722 748 (Pubitemid 46073481)
-
(2007)
Journal of Computational and Applied Mathematics
, vol.200
, Issue.2
, pp. 722-748
-
-
Rodal, J.1
Area, I.2
Godoy, E.3
-
46
-
-
38049060398
-
Structure relations for monic orthogonal polynomials in two discrete variables
-
J. Rodal, I. Area, and E. Godoy Structure relations for monic orthogonal polynomials in two discrete variables J. Math. Anal. Appl. 340 2 2008 825 844
-
(2008)
J. Math. Anal. Appl.
, vol.340
, Issue.2
, pp. 825-844
-
-
Rodal, J.1
Area, I.2
Godoy, E.3
-
48
-
-
0012584238
-
Orthogonal polynomials in two variables
-
Gordon and Breach Science Publishers, Amsterdam
-
P.K. Suetin, Orthogonal polynomials in two variables, vol. 3 of Analytical Methods and Special Functions, Gordon and Breach Science Publishers, Amsterdam, 1999.
-
(1999)
Analytical Methods and Special Functions
, vol.3
-
-
Suetin, P.K.1
-
49
-
-
0004073954
-
-
fourth ed. American Mathematical Society, Providence, RI American Mathematical Society, Colloquium Publications
-
G. Szego, Orthogonal polynomials, fourth ed., American Mathematical Society, Providence, RI, 1975, American Mathematical Society, Colloquium Publications, vol. XXIII.
-
(1975)
Orthogonal Polynomials
, vol.23
-
-
Szego, G.1
-
50
-
-
0011030664
-
Beitrage zur theorie der durch die heinesche reihe
-
J. Thomae Beitrage zur theorie der durch die heinesche reihe J. Reine Angew. Math. 70 1869 258 281
-
(1869)
J. Reine Angew. Math.
, vol.70
, pp. 258-281
-
-
Thomae, J.1
-
51
-
-
0009206913
-
Some multivariable orthogonal polynomials of the Askey tableau-continuous families
-
M.V. Tratnik Some multivariable orthogonal polynomials of the Askey tableau-continuous families J. Math. Phys. 32 8 1991 2065 2073
-
(1991)
J. Math. Phys.
, vol.32
, Issue.8
, pp. 2065-2073
-
-
Tratnik, M.V.1
-
52
-
-
0009125166
-
Some multivariable orthogonal polynomials of the Askey tableau-discrete families
-
M.V. Tratnik Some multivariable orthogonal polynomials of the Askey tableau-discrete families J. Math. Phys. 32 9 1991 2337 2342
-
(1991)
J. Math. Phys.
, vol.32
, Issue.9
, pp. 2337-2342
-
-
Tratnik, M.V.1
-
53
-
-
0041112892
-
Self-dual Koornwinder-Macdonald polynomials
-
J.F. van Diejen Self-dual Koornwinder-Macdonald polynomials Invent. Math. 126 2 1996 319 339 (Pubitemid 126323252)
-
(1996)
Inventiones Mathematicae
, vol.126
, Issue.2
, pp. 319-339
-
-
Van Diejen, J.F.1
-
54
-
-
0004076337
-
Representation of Lie groups and special functions
-
Kluwer Academic Publishers Group, Dordrecht
-
N.J. Vilenkin, A.U. Klimyk, Representation of Lie groups and special functions, vol. 316 of Mathematics and its Applications, Kluwer Academic Publishers Group, Dordrecht, 1995.
-
(1995)
Mathematics and Its Applications
, vol.316
-
-
Vilenkin, N.J.1
Klimyk, A.U.2
-
55
-
-
0347185339
-
On multivariate orthogonal polynomials
-
Y. Xu On multivariate orthogonal polynomials SIAM J. Math. Anal. 24 3 1993 783 794
-
(1993)
SIAM J. Math. Anal.
, vol.24
, Issue.3
, pp. 783-794
-
-
Xu, Y.1
-
56
-
-
84966248605
-
Multivariate orthogonal polynomials and operator theory
-
Y. Xu Multivariate orthogonal polynomials and operator theory Trans. Amer. Math. Soc. 343 1 1994 193 202
-
(1994)
Trans. Amer. Math. Soc.
, vol.343
, Issue.1
, pp. 193-202
-
-
Xu, Y.1
-
57
-
-
4344712043
-
On discrete orthogonal polynomials of several variables
-
DOI 10.1016/j.aam.2004.03.002, PII S0196885804000405
-
Y. Xu On discrete orthogonal polynomials of several variables Adv. Appl. Math. 33 3 2004 615 632 (Pubitemid 39150893)
-
(2004)
Advances in Applied Mathematics
, vol.33
, Issue.3
, pp. 615-632
-
-
Xu, Y.1
-
58
-
-
16244408065
-
Second-order difference equations and discrete orthogonal polynomials of two variables
-
Y. Xu Second-order difference equations and discrete orthogonal polynomials of two variables Int. Math. Res. Not. 8 2005 449 475 (Pubitemid 40466000)
-
(2005)
International Mathematics Research Notices
, Issue.8
, pp. 449-475
-
-
Xu, Y.1
-
59
-
-
79952046024
-
Image description with nonseparable two-dimensional Charlier and Meixner moments
-
H. Zhu, M. Liu, Y. Li, H. Shu, and H. Zhang Image description with nonseparable two-dimensional Charlier and Meixner moments Int. J. Pattern Recognit. Artif. Intell. 25 1 2011 37 55
-
(2011)
Int. J. Pattern Recognit. Artif. Intell.
, vol.25
, Issue.1
, pp. 37-55
-
-
Zhu, H.1
Liu, M.2
Li, Y.3
Shu, H.4
Zhang, H.5
|