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- Generating function (2)
- Bell number (1)
- Bernoulli number (1)
- Bernoulli polynomial (1)
- Bernstein-B´ezier polynomials (1)
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- Binomial enumeration (1)
- Delta operator (1)
- Euler number (1)
- Euler polynomial (1)
- Eulerian fraction (1)
- Euler’s series transform. (1)
- Formal power series (1)
- Fourier transform (1)
- Generalized weighted Stirling numbers (1)
- Genocchi number (1)
- Minimal support (1)
- Power series (1)
- Quasi-minimal support (1)
- Refinement. (1)
- Riodan array (1)
- Riordan group. (1)
- Sheffer group (1)
- Sheffer-type differential operators (1)
- Sheffer-type polynomials (1)
- Shift-invariant operator (1)
- Symbolic sum formula (1)
- Symbolic summation operator (1)
Articles 1 - 4 of 4
Full-Text Articles in Mathematics
Symbolization Of Generating Functions; An Application Of The Mullin–Rota Theory Of Binomial Enumeration, Tian-Xiao He, Peter J.S. S, Leetsch C. Hsu
Symbolization Of Generating Functions; An Application Of The Mullin–Rota Theory Of Binomial Enumeration, Tian-Xiao He, Peter J.S. S, Leetsch C. Hsu
Tian-Xiao He
We have found that there are more than a dozen classical generating functions that could be suitably symbolized to yield various symbolic sum formulas by employing the Mullin–Rota theory of binomial enumeration. Various special formulas and identities involving well-known number sequences or polynomial sequences are presented as illustrative examples. The convergence of the symbolic summations is discussed.
Fourier Transform Of Bernstein–Bézier Polynomials, Tian-Xiao He, Charles K. Chui, Qingtang Jiang
Fourier Transform Of Bernstein–Bézier Polynomials, Tian-Xiao He, Charles K. Chui, Qingtang Jiang
Tian-Xiao He
Explicit formulae, in terms of Bernstein–Bézier coefficients, of the Fourier transform of bivariate polynomials on a triangle and univariate polynomials on an interval are derived in this paper. Examples are given and discussed to illustrate the general theory. Finally, this consideration is related to the study of refinement masks of spline function vectors.
Construction Of Biorthogonal B-Spline Type Wavelet Sequences With Certain Regularities, Tian-Xiao He
Construction Of Biorthogonal B-Spline Type Wavelet Sequences With Certain Regularities, Tian-Xiao He
Tian-Xiao He
No abstract provided.
The Sheffer Group And The Riordan Group, Tian-Xiao He, Peter J.S. Shiue, Leetsch C. Hsu
The Sheffer Group And The Riordan Group, Tian-Xiao He, Peter J.S. Shiue, Leetsch C. Hsu
Tian-Xiao He
We define the Sheffer group of all Sheffer-type polynomials and prove the isomorphism between the Sheffer group and the Riordan group. An equivalence of the Riordan array pair and generalized Stirling number pair is also presented. Finally, we discuss a higher dimensional extension of Riordan array pairs.