I have the following formula for KummerU:
U = gamma(1-b)*KummerMz(a,b,z)/gamma(a-b+1) + gamma(b-1)*z.^(1-b).*KummerMz(a-b+1,2-b,z)/gamma(a)
from [https://pmc.polytechnique.fr/pagesperso/dg/confluent/KummerU.m][1]
I am generating it in Excel using a Gamma and KummerM function. But I do not get the desired score of .953742 for a=.25, b=.25, z=.5.
Any input to where the calculation is going wrong?
I cannot tell where is your error.
Your expression is $$U(a,b,z)=\frac{\Gamma (1-b) }{\Gamma (a-b+1)}\, _1F_1(a;b;z)+z^{1-b}\frac{ \Gamma (b-1)}{\Gamma (a)} \, _1F_1(a-b+1;2-b;z)$$
For the values you give $(a=b=\frac 14,\,z=\frac 12)$, this reduces to $$\sqrt{e}\,\, \Gamma \left(\frac{3}{4},\frac{1}{2}\right)\approx 0.953742$$
The two numerical values you wrote in comments are correct.