Definition:monicBesselPoly

From DRMF
Revision as of 00:33, 6 March 2017 by imported>SeedBot (DRMF)
Jump to navigation Jump to search

The LaTeX DLMF and DRMF macro \monicBesselPoly represents the monic Bessel polynomial.

This macro is in the category of polynomials.

In math mode, this macro can be called in the following ways:

\monicBesselPoly{n} produces y ^ n Bessel-polynomial-monic-p 𝑛 {\displaystyle{\displaystyle{\displaystyle{\widehat{y}}_{n}}}}
\monicBesselPoly{n}@{x}{a} produces y ^ n ⁑ ( x ; a ) Bessel-polynomial-monic-p 𝑛 π‘₯ π‘Ž {\displaystyle{\displaystyle{\displaystyle{\widehat{y}}_{n}\!\left(x;a\right)}}}
\monicBesselPoly{n}@@{x}{a} produces y ^ n ⁑ ( x ) Bessel-polynomial-monic-p 𝑛 π‘₯ π‘Ž {\displaystyle{\displaystyle{\displaystyle{\widehat{y}}_{n}\!\left(x\right)}}}

These are defined by y n ⁑ ( x ; a ) = : ( n + a + 1 ) n 2 n y ^ n ⁑ ( x ; a ) fragments Bessel-polynomial-y 𝑛 π‘₯ π‘Ž : Pochhammer-symbol 𝑛 π‘Ž 1 𝑛 superscript 2 𝑛 Bessel-polynomial-monic-p 𝑛 π‘₯ π‘Ž {\displaystyle{\displaystyle{\displaystyle y_{n}\!\left(x;a\right)=:\frac{{% \left(n+a+1\right)_{n}}}{2^{n}}{\widehat{y}}_{n}\!\left(x;a\right)}}}

Symbols List

y ^ n subscript ^ 𝑦 𝑛 {\displaystyle{\displaystyle{\displaystyle{\widehat{y}}_{n}}}}  : monic Bessel polynomial : http://drmf.wmflabs.org/wiki/Definition:monicBesselPoly
y n subscript 𝑦 𝑛 {\displaystyle{\displaystyle{\displaystyle y_{n}}}}  : Bessel polynomial : http://dlmf.nist.gov/18.34#E1
( a ) n subscript π‘Ž 𝑛 {\displaystyle{\displaystyle{\displaystyle(a)_{n}}}}  : Pochhammer symbol : http://dlmf.nist.gov/5.2#iii