Hi everyone! I have a differential equation of the form
The solutions to this equation are the parabolic cylinder functions. Using the definition as stated in Wikipedia, the even and odd solutions are and , respectively. For real, nonzero values of , these solutions are oscillating with decreasing amplitude and period. I am interested in calculating the value of
as a function of . With the normalization as used in the Wikipedia article, this value is a positive and finite constant (when ). I found numerically for that this value is . Can anyone help me with this problem?