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Application of Eigenkets of Bosonic Creation Operator in Deriving Some New Formulas of Associated Laguerre Polynomials

Using the resolution of unity composed of bosonic creation operator's eigenkets and annihilation operator's un-normalized eigenket, which is a new quantum mechanical representation in contour integration form, we derive new contour integration expression of associated Laguerre polynomials Lρm(|z|2) and its generalized generating function formula. A series of recursive relations regarding to Lρm(|z|2) are also deduced in the context of the Fock representation by algebraic method.