메뉴 건너뛰기




Volumn 112, Issue , 2004, Pages 199-235

Some results for q-functions of many variables

Author keywords

[No Author keywords available]

Indexed keywords


EID: 33744989803     PISSN: 00418994     EISSN: 22402926     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (16)

References (77)
  • 1
    • 0001048350 scopus 로고
    • Canonical equations and symmetry techniques for q-series
    • A. K. Agarwal - E. G. Kalnins - W. Jr. Miller, Canonical equations and symmetry techniques for q-series, SIAM J. Math. Anal., 18, 6 (1987), pp. 1519-1538.
    • (1987) SIAM J. Math. Anal , vol.18 , Issue.6 , pp. 1519-1538
    • Agarwal, A.K.1    Kalnins, E.G.2    Miller, W.3
  • 2
    • 20244380629 scopus 로고
    • Some Basic Hypergeometric Identities
    • R. P. Agarwal, Some Basic Hypergeometric Identities, Ann. Soc. Sci. Bruxelles. Ser. I, 67 (1953), pp. 186-202.
    • (1953) Ann. Soc. Sci. Bruxelles. Ser. I , vol.67 , pp. 186-202
    • Agarwal, R.P.1
  • 3
    • 51249195549 scopus 로고
    • Some Relations between Basic Hypergeometric Functions of Two Variables
    • R. P. Agarwal, Some Relations between Basic Hypergeometric Functions of Two Variables, Rend. Circ. Mat. Palermo (2), 3 (1954), pp. 76-82.
    • (1954) Rend. Circ. Mat. Palermo (2) , vol.3 , pp. 76-82
    • Agarwal, R.P.1
  • 4
    • 84979326045 scopus 로고
    • q-Bernoulli Numbers and Polynomials
    • W. A. Al-Salam, q-Bernoulli Numbers and Polynomials, Math. Nachr., 17 (1959), pp. 239-260.
    • (1959) Math. Nachr , vol.17 , pp. 239-260
    • Al-Salam, W.A.1
  • 5
    • 84963009064 scopus 로고
    • Saalschützian theorems for basic double series
    • W. A. Al-Salam, Saalschützian theorems for basic double series, J. London Math. Soc., 40 (1965), pp. 455-458.
    • (1965) J. London Math. Soc , vol.40 , pp. 455-458
    • Al-Salam, W.A.1
  • 6
    • 0011011707 scopus 로고
    • Summations and transformations for basic Appell series
    • G. E. Andrews, Summations and transformations for basic Appell series, J. London Math. Soc. (2), 4 (1972), pp. 618-622.
    • (1972) J. London Math. Soc. (2) , vol.4 , pp. 618-622
    • Andrews, G.E.1
  • 7
    • 0042370081 scopus 로고
    • Sur des séries hypergéométriques de deux variables …
    • P. Appell, Sur des séries hypergéométriques de deux variables … C. R. Paris, 90 (1880), pp. 296-298, 731-734.
    • (1880) C. R. Paris , vol.90
    • Appell, P.1
  • 9
    • 0000994135 scopus 로고
    • A note on certain q-identities
    • W. N. Bailey, A note on certain q-identities, Quarterly J. Math., 12 (1941), pp. 173-175.
    • (1941) Quarterly J. Math , vol.12 , pp. 173-175
    • Bailey, W.N.1
  • 11
    • 0010896915 scopus 로고
    • Expansions of Appell's double hypergeometric functions
    • J. L. Burchnall - T. W. Chaundy, Expansions of Appell's double hypergeometric functions, Quart. J. Math., 11 (1940), pp. 249-270.
    • (1940) Quart. J. Math , vol.11 , pp. 249-270
    • Burchnall, J.L.1    Chaundy, T.W.2
  • 12
    • 0004552793 scopus 로고
    • Expansions of Appell's double hypergeometric functions. II
    • J. L. Burchnall - T. W. Chaundy, Expansions of Appell's double hypergeometric functions. II, Quart. J. Math., 12 (1941), pp. 112-128.
    • (1941) Quart. J. Math , vol.12 , pp. 112-128
    • Burchnall, J.L.1    Chaundy, T.W.2
  • 13
    • 46749105426 scopus 로고
    • A Saalschützian theorem for double series
    • L. Carlitz, A Saalschützian theorem for double series, J. London Math. Soc., 38 (1963), pp. 415-418.
    • (1963) J. London Math. Soc , vol.38 , pp. 415-418
    • Carlitz, L.1
  • 14
    • 84915723326 scopus 로고
    • A summation theorem for double hypergeometric series
    • L. Carlitz, A summation theorem for double hypergeometric series, Rend. Sem. Mat. Univ. Padova, 37 (1967), pp. 230-233.
    • (1967) Rend. Sem. Mat. Univ. Padova , vol.37 , pp. 230-233
    • Carlitz, L.1
  • 15
    • 84968510871 scopus 로고
    • The need for a new classification of double hypergeometric series
    • B. C. Carlson, The need for a new classification of double hypergeometric series, Proc. Amer. Math. Soc., 56 (1976), pp. 221-224.
    • (1976) Proc. Amer. Math. Soc , vol.56 , pp. 221-224
    • Carlson, B.C.1
  • 16
    • 0001811457 scopus 로고
    • Operatormethoden für q-Identitäten
    • J. Cigler, Operatormethoden für q-Identitäten, Monatshefte für Mathematik, 88 (1979), pp. 87-105.
    • (1979) Monatshefte für Mathematik , vol.88 , pp. 87-105
    • Cigler, J.1
  • 18
    • 0007931752 scopus 로고
    • The basic analog of Kummers theorem
    • J. A. Daum, The basic analog of Kummers theorem, Bull. Amer. Math. Soc., 48 (1942), pp. 711-713.
    • (1942) Bull. Amer. Math. Soc , vol.48 , pp. 711-713
    • Daum, J.A.1
  • 19
    • 20244367310 scopus 로고
    • Summation of a certain series
    • A. C. Dixon, Summation of a certain series, Proc. London Math. Soc. (1), 35 (1903), pp. 285-289.
    • (1903) Proc. London Math. Soc. (1) , vol.35 , pp. 285-289
    • Dixon, A.C.1
  • 23
    • 0242275202 scopus 로고    scopus 로고
    • A method for q-calculus
    • T. Ernst, A method for q-calculus, J. nonlinear Math. Physics, 10, No. 4 (2003), pp. 487-525.
    • (2003) J. nonlinear Math. Physics , vol.10 , Issue.4 , pp. 487-525
    • Ernst, T.1
  • 28
    • 0003180796 scopus 로고
    • General hypergeometric systems of equations and series of hypergeometric type
    • (Russian) (286), 235 translation in Russian Math. Surveys, 47, no. 4 (1992), pp. 1-88
    • I. M. Gelfand - M. I. Graev - V. S. Retakh, General hypergeometric systems of equations and series of hypergeometric type. (Russian) Uspekhi Mat. Nauk, 47, no. 4 (1992), (286), pp. 3-82, 235 translation in Russian Math. Surveys, 47, no. 4 (1992), pp. 1-88.
    • (1992) Uspekhi Mat. Nauk , vol.47 , Issue.4 , pp. 3-82
    • Gelfand, I.M.1    Graev, M.I.2    Retakh, V.S.3
  • 30
    • 39049103535 scopus 로고
    • Transformation formulae for hypergeometric series in two variables. II
    • C. C. Grosjean - R. K. Sharma, Transformation formulae for hypergeometric series in two variables. II, Simon Stevin, 62, no. 2 (1988), pp. 97- 125.
    • (1988) Simon Stevin , vol.62 , Issue.2 , pp. 97-125
    • Grosjean, C.C.1    Sharma, R.K.2
  • 31
    • 0000243146 scopus 로고
    • Beiträge zur Theorie der Heineschen Reihen
    • W. Hahn, Beiträge zur Theorie der Heineschen Reihen, Mathematische Nachrichten, 2 (1949), pp. 340-379.
    • (1949) Mathematische Nachrichten , vol.2 , pp. 340-379
    • Hahn, W.1
  • 32
    • 0010299447 scopus 로고
    • Über die Reihe
    • E. Heine, Über die Reihe. J. reine angew. Math., 32 (1846), pp. 210- 212.
    • (1846) J. reine angew. Math , vol.32 , pp. 210-212
    • Heine, E.1
  • 33
    • 84941475777 scopus 로고
    • Untersuchungen über die Reihe
    • E. Heine, Untersuchungen über die Reihe. J. reine angew. Math., 34 (1847), pp. 285-328.
    • (1847) J. reine angew. Math , vol.34 , pp. 285-328
    • Heine, E.1
  • 35
    • 34447605654 scopus 로고
    • Über die Convergenz der hypergeometrischen Reihen zweier und dreier Veränderlichen
    • J. Horn, Über die Convergenz der hypergeometrischen Reihen zweier und dreier Veränderlichen, Mathematische Annalen, 34 (1889), pp. 544-600.
    • (1889) Mathematische Annalen , vol.34 , pp. 544-600
    • Horn, J.1
  • 36
    • 0002599674 scopus 로고
    • A generalization of the functions G(n) and x n
    • F. H. Jackson, A generalization of the functions G(n) and x n, Proc. Roy Soc. London, 74 (1904), pp. 64-72.
    • (1904) Proc. Roy Soc. London , vol.74 , pp. 64-72
    • Jackson, F.H.1
  • 37
    • 0002183689 scopus 로고
    • On generalized functions of Legendre and Bessel
    • F. H. Jackson, On generalized functions of Legendre and Bessel, Trans. Roy Soc. Edin., 41 (1904), pp. 1-28.
    • (1904) Trans. Roy Soc. Edin , vol.41 , pp. 1-28
    • Jackson, F.H.1
  • 38
    • 0040497111 scopus 로고
    • Theorems relating to a generalisation of the Bessel-function
    • F. H. Jackson, Theorems relating to a generalisation of the Bessel-function, Trans. Roy Soc. Edin., 41 (1904), pp. 105-118.
    • (1904) Trans. Roy Soc. Edin , vol.41 , pp. 105-118
    • Jackson, F.H.1
  • 39
    • 84974497034 scopus 로고
    • On q-functions and a certain difference operator
    • F. H. Jackson, On q-functions and a certain difference operator, Trans. Roy Soc.Edin., 46 (1908), pp. 253-281.
    • (1908) Trans. Roy Soc.Edin , vol.46 , pp. 253-281
    • Jackson, F.H.1
  • 40
    • 0007190172 scopus 로고
    • Transformations of q-series
    • F. H. Jackson, Transformations of q-series, Mess. Math., 39 (1910), pp. 145-153.
    • (1910) Mess. Math , vol.39 , pp. 145-153
    • Jackson, F.H.1
  • 41
    • 20244382997 scopus 로고
    • On basic double hypergeometric functions
    • F. H. Jackson, On basic double hypergeometric functions, Quart. J. Math., 13 (1942), pp. 69-82.
    • (1942) Quart. J. Math , vol.13 , pp. 69-82
    • Jackson, F.H.1
  • 42
    • 0011610975 scopus 로고
    • Basic double hypergeometric functions
    • F. H. Jackson, Basic double hypergeometric functions, Quart. J. Math., 15 (1944), pp. 49-61.
    • (1944) Quart. J. Math , vol.15 , pp. 49-61
    • Jackson, F.H.1
  • 43
    • 39049173636 scopus 로고
    • Some general q-polynomial expansions for functions of several variables and their applications to certain q-orthogonal polynomials and q-Lauricella functions
    • V. K. Jain - H. M. Srivastava, Some general q-polynomial expansions for functions of several variables and their applications to certain q-orthogonal polynomials and q-Lauricella functions, Bull. Soc. Roy. Sci. Liege, 58, no. 1 (1989), pp. 13-24.
    • (1989) Bull. Soc. Roy. Sci. Liege , vol.58 , Issue.1 , pp. 13-24
    • Jain, V.K.1    Srivastava, H.M.2
  • 44
    • 38249011663 scopus 로고
    • New results involving a certain class of q-orthogonal polynomials
    • V. K. Jain - H. M. Srivastava, New results involving a certain class of q-orthogonal polynomials, J. Math. Anal. Appl., 166, no. 2 (1992), pp. 331- 344.
    • (1992) J. Math. Anal. Appl , vol.166 , Issue.2 , pp. 331-344
    • Jain, V.K.1    Srivastava, H.M.2
  • 46
    • 84933521058 scopus 로고
    • Reduction of certain hypergeometric functions of three variables
    • P. Karlsson, Reduction of certain hypergeometric functions of three variables, Glasnik Mat. Ser. III, 8 (28) (1973), pp. 199-204.
    • (1973) Glasnik Mat. Ser. III , vol.8 , Issue.28 , pp. 199-204
    • Karlsson, P.1
  • 47
    • 0030213650 scopus 로고    scopus 로고
    • Summations for basic hypergeometric series involving a q-analogue of the digamma function
    • C. Krattenthaler - H. M. Srivastava, Summations for basic hypergeometric series involving a q-analogue of the digamma function, Comput. Math. Appl., 32, no. 3 (1996), pp. 73-91.
    • (1996) Comput. Math. Appl , vol.32 , Issue.3 , pp. 73-91
    • Krattenthaler, C.1    Srivastava, H.M.2
  • 48
    • 84880641024 scopus 로고
    • Über die hypergeometrische Reihe …
    • E. E. Kummer, Über die hypergeometrische Reihe …, J. für Math., 15 (1836), pp. 39-83 and 127-172.
    • (1836) J. für Math , vol.15
    • Kummer, E.E.1
  • 49
    • 0011108717 scopus 로고    scopus 로고
    • Factorisation of Macdonald polynomials
    • (Canterbury, 1996), London Math. Soc. Lecture Note Ser., 255, Cambridge Univ. Press, Cambridge
    • V. B. Kuznetsov - E. K. Sklyanin, Factorisation of Macdonald polynomials, Symmetries and integrability of difference equations (Canterbury, 1996), pp. 370-384, London Math. Soc. Lecture Note Ser., 255, Cambridge Univ. Press, Cambridge, 1999.
    • (1999) Symmetries and integrability of difference equations , pp. 370-384
    • Kuznetsov, V.B.1    Sklyanin, E.K.2
  • 50
    • 11644322139 scopus 로고
    • Sulle Funzioni Ipergeometriche a piu Variabili
    • G. Lauricella, Sulle Funzioni Ipergeometriche a piu Variabili, Rend. Circ. Mat. Palermo, 7 (1893), pp. 111-158.
    • (1893) Rend. Circ. Mat. Palermo , vol.7 , pp. 111-158
    • Lauricella, G.1
  • 51
    • 0035646921 scopus 로고    scopus 로고
    • Transformation formulas for double hypergeometric series related to 9-j coefficients and their basic analogues
    • S. Lievens S. - J. Van der Jeugt, Transformation formulas for double hypergeometric series related to 9-j coefficients and their basic analogues, J. Math. Phys., 42 (2001), pp. 5417-5430.
    • (2001) J. Math. Phys , vol.42 , pp. 5417-5430
    • Lievens, S.-J.1    Van der Jeugt, S.2
  • 52
    • 0013317365 scopus 로고
    • Lie theory and Lauricella functions FD
    • W. Jr. Miller, Lie theory and Lauricella functions FD, J. Mathematical Phys., 13 (1972), pp. 1393-1399.
    • (1972) J. Mathematical Phys , vol.13 , pp. 1393-1399
    • Miller, W.1
  • 53
    • 3042610753 scopus 로고
    • Lie theory and the Appell functions F1
    • W. Jr Miller, Lie theory and the Appell functions F1, SIAM J. Math. Anal., 4 (1973), pp. 638-655.
    • (1973) SIAM J. Math. Anal , vol.4 , pp. 638-655
    • Miller, W.1
  • 54
    • 0038106952 scopus 로고
    • Some multiple series transformations
    • R. Panda, Some multiple series transformations, J nanabha Sect. A, 4 (1974), pp. 165-168.
    • (1974) J nanabha Sect. A , vol.4 , pp. 165-168
    • Panda, R.1
  • 56
    • 0004126854 scopus 로고
    • Reprint of 1960 first edition. Chelsea Publishing Co., Bronx, N.Y
    • E. D. Rainville, Special functions, Reprint of 1960 first edition. Chelsea Publishing Co., Bronx, N.Y., 1971.
    • (1971) Special functions
    • Rainville, E.D.1
  • 57
    • 84960605078 scopus 로고
    • On a three-fold symmetry in the elements of Heine's series
    • L. J. Rogers, On a three-fold symmetry in the elements of Heine's series, Proc. London Math. Soc., 24 (1893), pp. 171-179.
    • (1893) Proc. London Math. Soc , vol.24 , pp. 171-179
    • Rogers, L.J.1
  • 58
    • 84960566496 scopus 로고
    • On the expansion of some infinite products
    • L. J. Rogers, On the expansion of some infinite products, Proc. London Math. Soc., 24 (1893), pp. 337-352.
    • (1893) Proc. London Math. Soc , vol.24 , pp. 337-352
    • Rogers, L.J.1
  • 59
    • 20244390021 scopus 로고
    • Bemerkungen über die allgemeine hypergeometrische Reihe …
    • Anhang
    • P. Schafheitlin, Bemerkungen über die allgemeine hypergeometrische Reihe …, Arch. Math. Physik. (3), 19 (1912), Anhang 20-25.
    • (1912) Arch. Math. Physik. (3) , vol.19 , pp. 20-25
    • Schafheitlin, P.1
  • 63
    • 0040012114 scopus 로고
    • Hypergeometric functions of three variables
    • H. M. Srivastava, Hypergeometric functions of three variables, Ganita, 15 (1964), pp. 97-108.
    • (1964) Ganita , vol.15 , pp. 97-108
    • Srivastava, H.M.1
  • 64
    • 27844556479 scopus 로고
    • Certain pairs of inverse series relations
    • H. M. Srivastava, Certain pairs of inverse series relations, J. Reine Angew. Math., 245 (1970), pp. 47-54.
    • (1970) J. Reine Angew. Math , vol.245 , pp. 47-54
    • Srivastava, H.M.1
  • 66
    • 33744993986 scopus 로고
    • A note on certain summation theorems for multiple hypergeometric series
    • H. M. Srivastava, A note on certain summation theorems for multiple hypergeometric series, Simon Stevin, 52, no. 3 (1978), pp. 97-109.
    • (1978) Simon Stevin , vol.52 , Issue.3 , pp. 97-109
    • Srivastava, H.M.1
  • 67
    • 84894450862 scopus 로고
    • Some generalizations of Carlson's identity
    • H. M. Srivastava, Some generalizations of Carlson's identity, Boll. Un. Mat. Ital. A (5) 18, no. 1 (1981), pp. 138-143.
    • (1981) Boll. Un. Mat. Ital. A (5) , vol.18 , Issue.1 , pp. 138-143
    • Srivastava, H.M.1
  • 70
    • 17444396461 scopus 로고
    • Some transformations and reduction formulas for multiple q-hypergeometric series
    • H. M. Srivastava, Some transformations and reduction formulas for multiple q-hypergeometric series, Ann. Mat. Pura Appl. (4) 144 (1986), pp. 49- 56.
    • (1986) Ann. Mat. Pura Appl. (4) , vol.144 , pp. 49-56
    • Srivastava, H.M.1
  • 71
    • 0011030664 scopus 로고
    • Beiträge zur Theorie der durch die Heinische Reihe …
    • J. Thomae, Beiträge zur Theorie der durch die Heinische Reihe …, J. reine angew. Math., 70 (1869), pp. 258-281.
    • (1869) J. reine angew. Math , vol.70 , pp. 258-281
    • Thomae, J.1
  • 72
    • 33744994642 scopus 로고
    • Les séries Heinéennes supérieures
    • J. Thomae, Les séries Heinéennes supérieures, Ann. Mat. pura appl. Bologna, II, 4 (1871), pp. 105-139.
    • (1871) Ann. Mat. pura appl. Bologna, II , vol.4 , pp. 105-139
    • Thomae, J.1
  • 73
    • 0036468147 scopus 로고    scopus 로고
    • Transformation formula for a double Clausenian hypergeometric series, its q-analogue, and its invariance group
    • J. Van der Jeugt, Transformation formula for a double Clausenian hypergeometric series, its q-analogue, and its invariance group, J. Comp. Appl. Math., 139 (2002), pp. 65-73.
    • (2002) J. Comp. Appl. Math , vol.139 , pp. 65-73
    • Van der Jeugt, J.1
  • 74
    • 84972495883 scopus 로고
    • Certain expansions of generalised basic hypergeometric functions
    • A. Verma, Certain expansions of generalised basic hypergeometric functions, Duke Math. J., 31 (1964), pp. 79-90.
    • (1964) Duke Math. J , vol.31 , pp. 79-90
    • Verma, A.1
  • 75
    • 84968503361 scopus 로고
    • Expansions involving hypergeometric functions of two variables
    • A. Verma, Expansions involving hypergeometric functions of two variables, Math. Comp., 20 (1966), pp. 590-596.
    • (1966) Math. Comp , vol.20 , pp. 590-596
    • Verma, A.1
  • 76
    • 0009375219 scopus 로고
    • A calculus of sequences
    • M. Ward, A calculus of sequences, Amer. J. Math., 58 (1936), pp. 255- 266.
    • (1936) Amer. J. Math , vol.58 , pp. 255-266
    • Ward, M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.