1 |
R. Tremblay, S. Gaboury, and B.-J. Fugere, A new transformation formula for fractional derivatives with applications, Integral Transforms Spec. Funct. 24 (2013), no. 3, 172-186.
DOI
|
2 |
J. Touchard, Sur certaines equations fontionelles, Proc. Int. Cong. Math. Toronto 1924 (1928), 456-472.
|
3 |
R. Tremblay and B.-J. Fugere, Generating functions related to pairs of inverse functions, Transform methods & special functions, Varna '96, Bulgarian Acad. Sci., Sofia (1998), 484-495.
|
4 |
R. Tremblay, S. Gaboury, and B.-J. Fugere, A new Leibniz rule and its integral analogue for fractional derivatives, Integral Transforms Spec. Funct. 24 (2013), no. 2, 111-128.
DOI
|
5 |
R. Tremblay, S. Gaboury, and B.-J. Fugere, Taylor-like expansion in terms of a rational function obtained by means of fractional derivatives, Integral Transforms Spec. Funct. 24 (2013), no. 1, 50-64.
DOI
|
6 |
W. Wang, C. Jia, and T. Wang, Some results on the Apostol-Bernoulli and Apostol-Euler polynomials, Comput. Math. Appl. 55 (2008), no. 6, 1322-1332.
DOI
ScienceOn
|
7 |
G. Polya and G. Szego, Problems and Theorems in Analysis. Vol. 1, (Translated from the German by D. Aeppli), Springer-Verlag, New York, Heidelberg and Berlin, 1972.
|
8 |
T. J. Osler, Leibniz rule for fractional derivatives and an application to infinite series, SIAM J. Appl. Math. 18 (1970), 658-674.
DOI
ScienceOn
|
9 |
T. J. Osler, Leibniz rule, the chain rule and Taylor's theorem for fractional derivatives, Ph.D. thesis, New York University, 1970.
|
10 |
T. J. Osler, A further extension of the Leibniz rule to fractional derivatives and its relation to Parseval's formula, SIAM J. Math. Anal. 3 (1972), 1-16.
DOI
|
11 |
H. M. Srivastava, Some generalizations of Carlitz's theorem, Pacific J. Math. 85 (1979), no. 2, 471-477.
DOI
|
12 |
H. M. Srivastava, Some bilateral generating functions for a certain class of special functions. I, II, Nederl. Akad. Wetensch. Indag. Math. 42 (1980), no. 2, 221-233, 234-246.
|
13 |
H. M. Srivastava, Some generating functions for Laguerre and Bessel polynomials, Bull. Inst. Math. Acad. Sinica (1980), no. 4, 571-579.
|
14 |
H. M. Srivastava, Some formulas for the Bernoulli and Euler polynomials at rational arguments, Math. Proc. Cambridge Philos. Soc. 129 (2000), no. 1, 77-84.
DOI
ScienceOn
|
15 |
N. E. Norlund, Vorlesungen der differenzenrechnung, Sringer, Berlin, 1924.
|
16 |
H. M. Srivastava and H. L. Manocha, A treatise on generating functions, Transform methods & special functions, Varna '96, 484-495, Bulgarian Acad. Sci., Sofia, 1998.
|
17 |
H. M. Srivastava and J. P. Singhal, New generating functions for Jacobi and related polynomials, J. Math. Anal. Appl. 41 (1973), 748-752.
DOI
|
18 |
H. M. Srivastava, M. Garg, and S. Choudhary, A new generalization of the Bernoulli and related polynomials, Russ. J. Math. Phys. 17 (2010), no. 2, 251-261.
DOI
|
19 |
H. M. Srivastava, M. Garg, and S. Choudhary, Some new families of generalized Euler and Genocchi polynomials, Taiwanese J. Math. 15 (2011), no. 1, 283-305.
DOI
|
20 |
H. M. Srivastava and A. Pinter, Remarks on some relationships between the Bernoulli and Euler polynomials, Appl. Math. Lett. 17 (2004), no. 4, 375-380.
DOI
ScienceOn
|
21 |
M. Garg, K. Jain, and H. M. Srivastava, Some relationships between the generalized apostol-bernoulli polynomials and Hurwitz-Lerch zeta functions, Integral Transform Spec. Funct. 17 (2006), no. 11, 803-815.
DOI
ScienceOn
|
22 |
L. Carlitz and H. M. Srivastava, Some new generating functions for the Hermite polynomials, J. Math. Anal. Appl. 149 (1990), 513-520.
DOI
|
23 |
R. Donaghey, Two transformations of series that commute with compositional inversion, J. Combin. Theory Ser. A 27 (1979), no. 3, 360-364.
DOI
|
24 |
A. Erdelyi, W. Magnus, F. Oberhettinger, and F. Tricomi, Higher Transcendental Functions. Vols. 1-3, New York, Toronto and London, McGraw-Hill Book Company, 1953.
|
25 |
Q.-M. Luo, The multiplication formulas for the apostol-bernoulli and Apostol-Euler polynomials of higher order, Integral Transform Spec. Funct. 20 (2009), no. 5-6, 377-391.
DOI
ScienceOn
|
26 |
J.-L. Lavoie, T. J. Osler, and R. Tremblay, Fundamental properties of fractional derivatives via Pochhammer integrals, Lecture Notes in Mathematics, 1974.
|
27 |
Y. Luke, The Special Functions and Their Approximations. Vols. 1-2, Mathematics in Science and Engineering, New York and London, Academic Press, 1969.
|
28 |
Q.-M. Luo, Apostol-Euler polynomials of higher order and Gaussian hypergeometric functions, Taiwanese J. Math. 10 (2006), no. 4, 917-925.
DOI
|
29 |
Q.-M. Luo, B.-N. Guo, F. Qui, and L. Debnath, Generalizations of Bernoulli numbers and polynomials, Int. J. Math. Math. Sci. 2003 (2003), no. 59, 3769-3776.
DOI
|
30 |
Q.-M. Luo and H. M. Srivastava, Some generalizations of the Apostol-Bernoulli and Apostol-Euler polynomials, J. Math. Anal. Appl. 308 (2005), no. 1, 290-302.
DOI
ScienceOn
|
31 |
Q.-M. Luo and H. M. Srivastava, Some relationships between the Apostol-Bernoulli and Apostol-Euler polynomials, Comput. Math. Appl. 51 (2006), no. 3-4, 631-642.
DOI
ScienceOn
|
32 |
N. Nielsen, Traite elementaire des nombres de bernoulli, Gauthier-Villars, Paris, 1923.
|
33 |
L. Carlitz, A class of generating functions, SIAM J. Math. Anal. 8 (1977), no. 3, 518-532.
DOI
|
34 |
L. Carlitz, Degenerate Stirling, Bernoulli and Eulerian numbers, Utilitas Math. 15 (1979), 51-88.
|
35 |
L. Carlitz, A degenerate Staudt-Clausen theorem, Arch. Math. 7 (1956), 28-33.
DOI
|
36 |
A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier, 2006.
|
37 |
T. J. Osler, Fractional derivatives of a composite function, SIAM J. Math. Anal. 1 (1970), 288-293.
DOI
|