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DLMF:18.12.E13

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Formula:6352
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MaRDI QIDQ6352

  • Label: DLMF:18.12.E13


Digital Library of Mathematical Functions ID 18.12.E13

( 1 - z ) - α - 1 ⁢ exp ⁡ ( x ⁢ z z - 1 ) = ∑ n = 0 ∞ L n ( α ) ⁡ ( x ) ⁢ z n , superscript 1 𝑧 𝛼 1 𝑥 𝑧 𝑧 1 superscript subscript 𝑛 0 Laguerre-polynomial-L 𝛼 𝑛 𝑥 superscript 𝑧 𝑛 {\displaystyle{\displaystyle(1-z)^{-\alpha-1}\exp\left(\frac{xz}{z-1}\right)=% \sum_{n=0}^{\infty}L^{(\alpha)}_{n}\left(x\right)z^{n},}}


Constraint(s)

| z | < 1 𝑧 1 {\displaystyle{\displaystyle|z|<1}}

Symbols List

  • L n ( α ) ⁡ ( x ) Laguerre-polynomial-L 𝛼 𝑛 𝑥 {\displaystyle{\displaystyle L^{(\NVar{\alpha})}_{\NVar{n}}\left(\NVar{x}% \right)}} : Laguerre (or generalized Laguerre) polynomial
  • exp ⁡ z 𝑧 {\displaystyle{\displaystyle\exp\NVar{z}}} : exponential function
  • z 𝑧 {\displaystyle{\displaystyle z}} : complex variable
  • n 𝑛 {\displaystyle{\displaystyle n}} : nonnegative integer
  • x 𝑥 {\displaystyle{\displaystyle x}} : real variable
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