The analytic expression of correlation function of free scalar field in any dimensional Euclidean space is derived by two different methods

the second of which is proposed. The results in 3 and lower dimensional space are generally discussed in the literature

and the generalized result in arbitrary dimensional space is obtained. When studying the case in 3dimensional space

people often do the integration directly in the 3dimensional space using the sphere coordinates

and this method is also applied in this paper to get the generalized result. On the other hand

it is found that choosing the appropriate coordinate system can effectively reduce the integration variable dimension and finally arrive at the same result. The result shows that the correlation function of free scalar field in any dimensional space is related to the modified Bessel function

whose order is determined by the space dimension.