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A new analytical method for the computation of reproducing kernel is proposed and tested on some examples. The expression ofreproducing kernel on infinite interval is obtained concisely in polynomial form for the first time. Furthermore, as a particular effective application of this method, we give an explicit representation formula for calculation of reproducing kernel in reproducing kernel space with boundary value conditions

A Novel Approach to Calculation of Reproducing Kernel on Infinite Interval and Applications to Boundary Value Problems