# Talk:Bessel polynomials

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## Consistent notation

The definition favored by mathematicians ... ${\displaystyle y_{n}(x)=...}$ Another definition, ... the reverse Bessel polynomials ... ${\displaystyle \theta _{n}(x)=...}$

Then later:

The Bessel polynomial may also be defined using Bessel functions ... where ... yn(x) is the reverse polynomial

Please use the same notation for ordinary vs reverse throughout.

• Wolfram uses y for ordinary "y_3(x) = 15x^3+15x^2+6x+1"
• OEIS uses "y_3(x) = 15*x^3 + 15*x^2 + 6*x + 1" for ordinary
• Krall and Frink 1948 says "the Bessel polynomial yn(x)" and lists an ordinary polynomial as increasing powers: "yn(x) = 1 + 6x + 15x^2 + 15x^3"
• Bessel Polynomials by E. Grosswald says "we shall adopt in general the original normalization of Krall and Frink" but then "the reverse polynomial yn(Z)"
• Berg-Vignat 2005 says "θn are sometimes called the reverse Bessel polynomials and yn (u) ... the ordinary Bessel polynomials."
• Campos and Calderón 2011 says "the Bessel polynomial yn (x). ... reverse Bessel polynomials θn (x)"

So it seems like most are in agreement that y is the ordinary and theta the reverse and Grosswald is the only exception? — Omegatron (talk) 02:38, 9 September 2015 (UTC)