Formula:KLS:09.10:03

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( c - 1 ) ⁢ x ⁢ M n ⁡ ( x ; β , c ) = c ⁢ ( n + β ) ⁢ M n + 1 ⁡ ( x ; β , c ) - [ n + ( n + β ) ⁢ c ] ⁢ M n ⁡ ( x ; β , c ) + n ⁢ M n - 1 ⁡ ( x ; β , c ) 𝑐 1 𝑥 Meixner-polynomial-M 𝑛 𝑥 𝛽 𝑐 𝑐 𝑛 𝛽 Meixner-polynomial-M 𝑛 1 𝑥 𝛽 𝑐 delimited-[] 𝑛 𝑛 𝛽 𝑐 Meixner-polynomial-M 𝑛 𝑥 𝛽 𝑐 𝑛 Meixner-polynomial-M 𝑛 1 𝑥 𝛽 𝑐 {\displaystyle{\displaystyle{\displaystyle(c-1)xM_{n}\!\left(x;\beta,c\right)=% c(n+\beta)M_{n+1}\!\left(x;\beta,c\right){}-\left[n+(n+\beta)c\right]M_{n}\!% \left(x;\beta,c\right)+nM_{n-1}\!\left(x;\beta,c\right)}}}

Proof

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Symbols List

M n subscript 𝑀 𝑛 {\displaystyle{\displaystyle{\displaystyle M_{n}}}}  : Meixner polynomial : http://dlmf.nist.gov/18.19#T1.t1.r9

Bibliography

Equation in Section 9.10 of KLS.

URL links

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