Generalized Werner's formula and the connection between trigonometry with target sum problems

This paper introduces the target sum function along with its characteristics. The target sum function takes a list of integers and a specific target integer as input values and expresses the number of ways to obtain the target sum by either adding or subtracting all of the integers from the given list. This function is rooted in the target sum problem which is explored in the fields of computer science and combinatorics. This paper, following the establishment of the generalized Werner's formula, will propose a link between the target sum function and the definite integral of the product of sine and cosine functions based on the formula.