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I have calculated below limit:

Limit[(a2 EllipticTheta[3, -((π (l + d0 g t))/(2 l)), E^(-((d0 π^2 t)/l^2))])/(2 Abs[l]) + ( a2 EllipticTheta[3, (π (l - d0 g t))/(2 l), E^(-((d0 π^2 t)/l^2))])/(2 Abs[l]) + ( a1 Sqrt[(d0 t)/l^2] EllipticTheta[3, -((d0 g π t)/(2 l)), E^(-((d0 π^2 t)/l^2))])/Sqrt[d0 t], l -> Infinity] 

The output is zero. However, if I put g=0; before limit funcion, the output is not zero anymore! Also when I run below piece of code:

a1 = 1; a2 = 1; g = 1.5; d0 = 1; t = 0.001; Plot[(a2 EllipticTheta[3, -((π (l + d0 g t))/(2 l)), E^(-((d0 π^2 t)/l^2))])/(2 Abs[l]) + ( a2 EllipticTheta[3, (π (l - d0 g t))/(2 l), E^(-((d0 π^2 t)/l^2))])/(2 Abs[l]) + ( a1 Sqrt[(d0 t)/l^2] EllipticTheta[3, -((d0 g π t)/(2 l)), E^(-((d0 π^2 t)/l^2))])/Sqrt[d0 t], {l, 100, 1000}] 

The output is not zero and doesn't goes to zero as I increase the "l". Could any one understand why does the output of limit is always zero? Can anyone help me to get the correct outcome of the Limit function?

I want to calculate the following limit:

Limit[(a2 EllipticTheta[3, -((π (l + d0 g t))/(2 l)), E^(-((d0 π^2 t)/l^2))])/(2 Abs[l]) + ( a2 EllipticTheta[3, (π (l - d0 g t))/(2 l), E^(-((d0 π^2 t)/l^2))])/(2 Abs[l]) + ( a1 Sqrt[(d0 t)/l^2] EllipticTheta[3, -((d0 g π t)/(2 l)), E^(-((d0 π^2 t)/l^2))])/Sqrt[d0 t], l -> Infinity] 

Mathematica gives an output of zero. However, if I put g=0; before using Limit, the output is not zero anymore! Also when I run the following piece of code:

a1 = 1; a2 = 1; g = 1.5; d0 = 1; t = 0.001; Plot[(a2 EllipticTheta[3, -((π (l + d0 g t))/(2 l)), E^(-((d0 π^2 t)/l^2))])/(2 Abs[l]) + ( a2 EllipticTheta[3, (π (l - d0 g t))/(2 l), E^(-((d0 π^2 t)/l^2))])/(2 Abs[l]) + ( a1 Sqrt[(d0 t)/l^2] EllipticTheta[3, -((d0 g π t)/(2 l)), E^(-((d0 π^2 t)/l^2))])/Sqrt[d0 t], {l, 100, 1000}] 

The output is not zero and doesn't go to zero as l increases. Can any one explain why Mathematica gives an incorrect output here? Can anyone help me to get the correct outcome of the Limit function?

I have calculated below limit:

 Limit[(a2 EllipticTheta[3, -((\[Pi] (l + d0 g t))/(2 l)), E^(-((d0 \[Pi]^2 t)/l^2))])/(2 Abs[l]) + ( a2 EllipticTheta[3, (\[Pi] (l - d0 g t))/(2 l), E^(-((d0 \[Pi]^2 t)/l^2))])/(2 Abs[l]) + ( a1 Sqrt[(d0 t)/l^2] EllipticTheta[3, -((d0 g \[Pi] t)/(2 l)), E^(-((d0 \[Pi]^2 t)/l^2))])/Sqrt[d0 t], l -> Infinity] 

The output is zero. However, if I put g=0; before limit funcion, the output is not zero anymore! Also when I run below piece of code:

a1 = 1; a2 = 1; g = 1.5; d0 = 1; t = 0.001; Plot[(a2 EllipticTheta[3, -((\[Pi] (l + d0 g t))/(2 l)), E^(-((d0 \[Pi]^2 t)/l^2))])/(2 Abs[l]) + ( a2 EllipticTheta[3, (\[Pi] (l - d0 g t))/(2 l), E^(-((d0 \[Pi]^2 t)/l^2))])/(2 Abs[l]) + ( a1 Sqrt[(d0 t)/l^2] EllipticTheta[3, -((d0 g \[Pi] t)/(2 l)), E^(-((d0 \[Pi]^2 t)/l^2))])/Sqrt[d0 t], {l, 100, 1000}] 

The output is not zero and doesn't goes to zero as I increase the "l". Could any one understand why does the output of limit is always zero? Can anyone help me to get the correct outcome of the Limit function?

I have calculated below limit:

Limit[(a2 EllipticTheta[3, -((π (l + d0 g t))/(2 l)), E^(-((d0 π^2 t)/l^2))])/(2 Abs[l]) + ( a2 EllipticTheta[3, (π (l - d0 g t))/(2 l), E^(-((d0 π^2 t)/l^2))])/(2 Abs[l]) + ( a1 Sqrt[(d0 t)/l^2] EllipticTheta[3, -((d0 g π t)/(2 l)), E^(-((d0 π^2 t)/l^2))])/Sqrt[d0 t], l -> Infinity] 

The output is zero. However, if I put g=0; before limit funcion, the output is not zero anymore! Also when I run below piece of code:

a1 = 1; a2 = 1; g = 1.5; d0 = 1; t = 0.001; Plot[(a2 EllipticTheta[3, -((π (l + d0 g t))/(2 l)), E^(-((d0 π^2 t)/l^2))])/(2 Abs[l]) + ( a2 EllipticTheta[3, (π (l - d0 g t))/(2 l), E^(-((d0 π^2 t)/l^2))])/(2 Abs[l]) + ( a1 Sqrt[(d0 t)/l^2] EllipticTheta[3, -((d0 g π t)/(2 l)), E^(-((d0 π^2 t)/l^2))])/Sqrt[d0 t], {l, 100, 1000}] 

The output is not zero and doesn't goes to zero as I increase the "l". Could any one understand why does the output of limit is always zero? Can anyone help me to get the correct outcome of the Limit function?