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Pidduck polynomials

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In mathematics, the Pidduck polynomials sn(x) are polynomials introduced by {{harvs|txt|last=Pidduck|year1=1910|year2=1912}} given by the generating function

:\displaystyle \sum_n \frac{s_n(x)}{n!}t^n = \left(\frac{1+t}{1-t}\right)^x(1-t)^{-1}

{{harv|Roman|1984|loc=4.4.3}}, {{harv|Boas|Buck|1958|loc=p.38}}

See also

References

  • {{Citation | last1=Boas | first1=Ralph P. | last2=Buck | first2=R. Creighton | title=Polynomial expansions of analytic functions | url=https://books.google.com/books?id=eihMuwkh4DsC | publisher=Springer-Verlag | location=Berlin, New York | series=Ergebnisse der Mathematik und ihrer Grenzgebiete. Neue Folge. | mr=0094466 | year=1958 | volume=19| isbn=978-0-387-03123-1 }}
  • {{Citation | last1=Pidduck | first1=F. B. | title=On the Propagation of a Disturbance in a Fluid under Gravity | jstor=92977 | publisher=The Royal Society | year=1910 | journal=Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character | issn=0950-1207 | volume=83 | issue=563 | pages=347–356 | doi=10.1098/rspa.1910.0023| url=https://zenodo.org/record/1432013 | doi-access=free | bibcode=1910RSPSA..83..347P }}
  • {{Citation | last1=Pidduck | first1=F. B. | title=The Wave-Problem of Cauchy and Poisson for Finite Depth and Slightly Compressible Fluid | jstor=93103 | publisher=The Royal Society | year=1912 | journal=Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character | issn=0950-1207 | volume=86 | issue=588 | pages=396–405 | doi=10.1098/rspa.1912.0031| doi-access=free | bibcode=1912RSPSA..86..396P }}
  • {{Citation | last1=Roman | first1=Steven | title=The umbral calculus | url=https://books.google.com/books?id=JpHjkhFLfpgC | publisher=Academic Press Inc. [Harcourt Brace Jovanovich Publishers] | location=London | series=Pure and Applied Mathematics | isbn=978-0-12-594380-2 | mr=741185 | year=1984 | volume=111}} Reprinted by Dover Publications, 2005

Category:Polynomials

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