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Corpus ID: 119151563

On Generating functions of Diagonals Sequences of Sheffer and Riordan Number Triangles

@article{Lang2017OnGF,
title={On Generating functions of Diagonals Sequences of Sheffer and Riordan Number Triangles},
author={Wolfdieter Lang},
journal={arXiv: Number Theory},
year={2017}
}

The exponential generating function of ordinary generating functions of diagonal sequences of general Sheffer triangles is computed by an application of Lagrange's theorem. For the special Jabotinsky type this is already known. An analogous computation for general Riordan number triangles leads to a formula for the logarithmic generating function of the ordinary generating functions of the product of the entries of the diagonal sequence of Pascal's triangle and those of the {Riordan triangle… Expand

Let $\left( a\left( x \right),xa\left( x \right) \right)$ is the Riordan matrix from the Bell subgroup. We denote ${{\left( a\left( x \right),xa\left( x \right) \right)}^{\varphi }}=\left(… Expand

For finite sums of non-negative powers of arithmetic progressions the generating functions (ordinary and exponential ones) for given powers are computed. This leads to a two parameter generalization… Expand

The On-Line Encyclopedia of Integer Sequences (or OEIS) is a database of some 130000 number sequences which serves as a dictionary, to tell the user what is known about a particular sequence and is widely used.Expand

The volume now gives a somewhat exhaustive account of the various ramifications of the subject, which are set out in an attractive manner and should become indispensable, not only as a textbook for advanced students, but as a work of reference to those whose aim is to extend the knowledge of analysis.Expand