expectation gaussian function of z, z is normally distributed

Hello,

this is my first post. I'm a phd student in Population genetics. I was reading a paper where the following is computed:

,

where:

and

The paper that I read (Lande 1983 equations 11a, 11b, Heredity - Abstract of article: The response to selection on major and minor mutations affecting a metrical trait) presents the result

.

where is just some constant.

I have tried for some hours to derive the last equation myself with no luck.

Could you help me please or provide some literature that I could read and learn how to do it?

best

idaios