Contact: +91-9711224068
International Journal of Applied Research
  • Multidisciplinary Journal
  • Printed Journal
  • Indexed Journal
  • Refereed Journal
  • Peer Reviewed Journal

ISSN Print: 2394-7500, ISSN Online: 2394-5869, CODEN: IJARPF

IMPACT FACTOR (RJIF): 8.4

Vol. 1, Issue 9, Part N (2015)

The invariance of the Hankel transform under K-Binomial transform of a sequence

The invariance of the Hankel transform under K-Binomial transform of a sequence

Author(s)
Parmod Kumar
Abstract
We give a new proof of the invariance of the Hankel transform under the binomial transform of a sequence. Our method of proof leads to three variations of the binomial transform; we call these the k-binomial transforms. We give a simple means of constructing these transforms via a triangle of numbers. We show how the exponential generating function of a sequence changes after our transforms are applied, and we use this to prove that several sequences in the On-Line Encyclopedia of Integer Sequences are related via our transforms. In the process, we prove three conjectures in the OEIS. Addressing a question of Layman, we then show that the Hankel transform of a sequence is invariant under one of our transforms, and we show how the Hankel transform changes after the other two transforms are applied. Finally, we use these results to determine the Hankel transforms of several integer sequences.
Pages: 930-933  |  1241 Views  128 Downloads


International Journal of Applied Research
How to cite this article:
Parmod Kumar. The invariance of the Hankel transform under K-Binomial transform of a sequence. Int J Appl Res 2015;1(9):930-933.
Call for book chapter
International Journal of Applied Research
Journals List Click Here Research Journals Research Journals