一类与算子有关的级数转化公式
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摘要
利用算子之间的相互关系将算子g(xΔ)展成3种不同的形式,构造一些级数转化公式,并结合Eulerian多项式简化这些级数转化公式、最后讨论这些级数转化公式在寻找求和公式及组合恒等式证明中的一些应用。
We expanded the operator g x()Δ in different ways,so as to construct some series-transformation formulas.And then,we simplified these formulas with Eulerian polynomial.Lastly,we discussed the application of these formulas which was used to prove combinational identities.
We expanded the operator g x()Δ in different ways,so as to construct some series-transformation formulas.And then,we simplified these formulas with Eulerian polynomial.Lastly,we discussed the application of these formulas which was used to prove combinational identities.
引文
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[3]He T X,Hsu L C,Shiue P J S.Convergence of the summation formulas constructed by using a symbolic operator approach[J].Computers and Mathematics with Applications,2006,51(3-4):441-450.
[4]He T X,Hsu L C,Shiue P J S.Symbolization of generating functions,an application of the Mullin–Rota theory of binomial enumeration[J].Computers and Mathematics with Applications,2007,(5):664-678.
[5]He T X,Hsu L C,Shiue P J S.A symbolic operator approach to several summation formulas for power series II[J].Discrete Mathematics,2008,308:3427-3440.
[6]Knopf P M.The operator(x/d/dx)n and its applications to series[J].Mathematics Magazine,2003,76(5):364-371.
[7]Comtet L.Advanced Combinatorics[M].Dordrecht:Springer,1974:204-212.
[8]Hsu L C,Shiue P J.On certain summation problem and generalization of Eulerian polynomials and numbers[J].Discrete Mathematics,1999,204(1-3):237-247.
[9]Boyadzhiev K N.A series transformation formula and related polynomials[J].International Journal of Mathematics and Mathematical Science,2005,23:3849-3866.
[2]He T X,Hsu L C,Shiue P J S.A symbolic operator approach to several summation formulas for power series[J].Computational and Applied Mathematics,2005,177:17-33.
[3]He T X,Hsu L C,Shiue P J S.Convergence of the summation formulas constructed by using a symbolic operator approach[J].Computers and Mathematics with Applications,2006,51(3-4):441-450.
[4]He T X,Hsu L C,Shiue P J S.Symbolization of generating functions,an application of the Mullin–Rota theory of binomial enumeration[J].Computers and Mathematics with Applications,2007,(5):664-678.
[5]He T X,Hsu L C,Shiue P J S.A symbolic operator approach to several summation formulas for power series II[J].Discrete Mathematics,2008,308:3427-3440.
[6]Knopf P M.The operator(x/d/dx)n and its applications to series[J].Mathematics Magazine,2003,76(5):364-371.
[7]Comtet L.Advanced Combinatorics[M].Dordrecht:Springer,1974:204-212.
[8]Hsu L C,Shiue P J.On certain summation problem and generalization of Eulerian polynomials and numbers[J].Discrete Mathematics,1999,204(1-3):237-247.
[9]Boyadzhiev K N.A series transformation formula and related polynomials[J].International Journal of Mathematics and Mathematical Science,2005,23:3849-3866.