Constant V

term[n_,x_,y_]:=  Sin[n π x] Exp[- n π y]

Plot3D[ term[1,x,y],{x,0,1},{y,0,1},PlotRange->All]

c[n_]=Integrate[  Sin[n π x]  ,{x,0,1}]

Limit[c[n],n->0]

c[0]=0

sum[m_,x_,y_]:=Sum[ c[n] term[n,x,y],{n,0,m}]

Plot3D[ sum[30,x,y],{x,0,1},{y,0,1},PlotRange->All]

BesselJ

Plot[Table[ BesselJ[n,r  ],{n,0,5}] //Evaluate,{r,0,10}]