In[]:=
Clear["Global`*"];​​​​Heat=
∂
t
T[y,t]-α
∂
{y,2}
T[y,t]==0;​​​​TraditionalForm[%];​​​​ic={T[y,0]==0,T[0,t]==1,(T[y,t]/.yInfinity)==0};​​​​sol[x_,t_]=FullSimplify[DSolveValue[{Heat,ic},T[y,t],{y,t}]]
Out[]=
1-
2
∞
∑
K[1]=1
0
π