A class of big (p,q)-Appell polynomials and their associated difference equations
In the present paper, we introduce and investigate the big (p,q)-Appell polynomials. We prove an equivalance theorem satisfied by the big (p, q)-Appell polynomials. As a special case of the big (p,q)- Appell polynomials, we present the corresponding equivalence theorem, recurrence relation and diffe...
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| Veröffentlicht in: | Filomat 2019, Vol.33 (10), p.3085-3121 |
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| creator | Srivastava, H.M. Yaşar, B.Y. Özarslan, M.A. |
| description | In the present paper, we introduce and investigate the big (p,q)-Appell
polynomials. We prove an equivalance theorem satisfied by the big (p,
q)-Appell polynomials. As a special case of the big (p,q)- Appell
polynomials, we present the corresponding equivalence theorem, recurrence
relation and difference equation for the big q-Appell polynomials. We also
present the equivalence theorem, recurrence relation and differential
equation for the usual Appell polynomials. Moreover, for the big (p;
q)-Bernoulli polynomials and the big (p; q)-Euler polynomials, we obtain
recurrence relations and difference equations. In the special case when p =
1, we obtain recurrence relations and difference equations which are
satisfied by the big q-Bernoulli polynomials and the big q-Euler
polynomials. In the case when p = 1 and q ? 1-, the big (p,q)-Appell
polynomials reduce to the usual Appell polynomials. Therefore, the
recurrence relation and the difference equation obtained for the big (p;
q)-Appell polynomials coincide with the recurrence relation and differential
equation satisfied by the usual Appell polynomials. In the last section, we
have chosen to also point out some obvious connections between the (p;
q)-analysis and the classical q-analysis, which would show rather clearly
that, in most cases, the transition from a known q-result to the
corresponding (p,q)-result is fairly straightforward.
nema |
| doi_str_mv | 10.2298/FIL1910085S |
| format | Article |
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polynomials. We prove an equivalance theorem satisfied by the big (p,
q)-Appell polynomials. As a special case of the big (p,q)- Appell
polynomials, we present the corresponding equivalence theorem, recurrence
relation and difference equation for the big q-Appell polynomials. We also
present the equivalence theorem, recurrence relation and differential
equation for the usual Appell polynomials. Moreover, for the big (p;
q)-Bernoulli polynomials and the big (p; q)-Euler polynomials, we obtain
recurrence relations and difference equations. In the special case when p =
1, we obtain recurrence relations and difference equations which are
satisfied by the big q-Bernoulli polynomials and the big q-Euler
polynomials. In the case when p = 1 and q ? 1-, the big (p,q)-Appell
polynomials reduce to the usual Appell polynomials. Therefore, the
recurrence relation and the difference equation obtained for the big (p;
q)-Appell polynomials coincide with the recurrence relation and differential
equation satisfied by the usual Appell polynomials. In the last section, we
have chosen to also point out some obvious connections between the (p;
q)-analysis and the classical q-analysis, which would show rather clearly
that, in most cases, the transition from a known q-result to the
corresponding (p,q)-result is fairly straightforward.
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polynomials. We prove an equivalance theorem satisfied by the big (p,
q)-Appell polynomials. As a special case of the big (p,q)- Appell
polynomials, we present the corresponding equivalence theorem, recurrence
relation and difference equation for the big q-Appell polynomials. We also
present the equivalence theorem, recurrence relation and differential
equation for the usual Appell polynomials. Moreover, for the big (p;
q)-Bernoulli polynomials and the big (p; q)-Euler polynomials, we obtain
recurrence relations and difference equations. In the special case when p =
1, we obtain recurrence relations and difference equations which are
satisfied by the big q-Bernoulli polynomials and the big q-Euler
polynomials. In the case when p = 1 and q ? 1-, the big (p,q)-Appell
polynomials reduce to the usual Appell polynomials. Therefore, the
recurrence relation and the difference equation obtained for the big (p;
q)-Appell polynomials coincide with the recurrence relation and differential
equation satisfied by the usual Appell polynomials. In the last section, we
have chosen to also point out some obvious connections between the (p;
q)-analysis and the classical q-analysis, which would show rather clearly
that, in most cases, the transition from a known q-result to the
corresponding (p,q)-result is fairly straightforward.
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polynomials. We prove an equivalance theorem satisfied by the big (p,
q)-Appell polynomials. As a special case of the big (p,q)- Appell
polynomials, we present the corresponding equivalence theorem, recurrence
relation and difference equation for the big q-Appell polynomials. We also
present the equivalence theorem, recurrence relation and differential
equation for the usual Appell polynomials. Moreover, for the big (p;
q)-Bernoulli polynomials and the big (p; q)-Euler polynomials, we obtain
recurrence relations and difference equations. In the special case when p =
1, we obtain recurrence relations and difference equations which are
satisfied by the big q-Bernoulli polynomials and the big q-Euler
polynomials. In the case when p = 1 and q ? 1-, the big (p,q)-Appell
polynomials reduce to the usual Appell polynomials. Therefore, the
recurrence relation and the difference equation obtained for the big (p;
q)-Appell polynomials coincide with the recurrence relation and differential
equation satisfied by the usual Appell polynomials. In the last section, we
have chosen to also point out some obvious connections between the (p;
q)-analysis and the classical q-analysis, which would show rather clearly
that, in most cases, the transition from a known q-result to the
corresponding (p,q)-result is fairly straightforward.
nema</abstract><doi>10.2298/FIL1910085S</doi><tpages>37</tpages><oa>free_for_read</oa></addata></record> |
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| language | eng |
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| title | A class of big (p,q)-Appell polynomials and their associated difference equations |
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