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I've come across an issue while using Wolfram Mathematica that I don't quite understand.

Consider the following symbolic computation:

Clear[n, y, x]; Sum[1/(n + y)^x, {n, 0, Infinity}]
 

Mathematica returns: "HurwitzZeta[x, y]"

However, when I plug in specific values (x = 1/3, y = 1) to evaluate the sum:

x = 1/3; y = 1; Sum[1/(n + y)^x, {n, 0, Infinity}]

I get an error message: "Sum::div: Sum does not converge."

What confuses me is when I compute HurwitzZeta[1/3, 1] // N, it successfully returns a numerical value: -0.97336.

So, why does the Sum function claim the series doesn't converge, but HurwitzZeta, which should be equivalent according to Mathematica's own symbolic computation, computes a numerical value without issue? Can anyone shed some light on this discrepancy or at least on what I am missing?

I've come across an issue while using Wolfram Mathematica that I don't quite understand.

Consider the following symbolic computation:

Clear[n, y, x]; 
Sum[1/(n + y)^x, {n, 0, Infinity}]

HurwitzZeta[x, y]

However, when I plug in specific values (x = 1/3, y = 1) to evaluate the sum:

x = 1/3; y = 1;  
Sum[1/(n + y)^x, {n, 0, Infinity}]

I get an error message:

"Sum::div: Sum does not converge."

What confuses me is when I compute HurwitzZeta[1/3, 1] // N, it successfully returns a numerical value: -0.97336.

So, why does the Sum function claim the series doesn't converge, but HurwitzZeta, which should be equivalent according to Mathematica's own symbolic computation, computes a numerical value without issue? Can anyone shed some light on this discrepancy or at least on what I am missing?

I've come across an issue while using Wolfram Mathematica that I don't quite understand.

Consider the following symbolic computation:

Clear[n, y, x]; Sum[1/(n + y)^x, {n, 0, Infinity}]

Mathematica returns: "HurwitzZeta[x, y]"

However, when I plug in specific values (x = 1/3, y = 1) to evaluate the sum:

x = 1/3; y = 1; Sum[1/(n + y)^x, {n, 0, Infinity}]

I get an error message: "Sum::div: Sum does not converge."

What confuses me is when I compute HurwitzZeta[1/3, 1] // N, it successfully returns a numerical value:  1.082409227768647*10^18635.

So, why does the Sum function claim the series doesn't converge, but HurwitzZeta, which should be equivalent according to Mathematica's own symbolic computation, computes a numerical value without issue? Can anyone shed some light on this discrepancy or at least on what I am missing?

I've come across an issue while using Wolfram Mathematica that I don't quite understand.

Consider the following symbolic computation:

Clear[n, y, x]; Sum[1/(n + y)^x, {n, 0, Infinity}]

Mathematica returns: "HurwitzZeta[x, y]"

However, when I plug in specific values (x = 1/3, y = 1) to evaluate the sum:

x = 1/3; y = 1; Sum[1/(n + y)^x, {n, 0, Infinity}]

I get an error message: "Sum::div: Sum does not converge."

What confuses me is when I compute HurwitzZeta[1/3, 1] // N, it successfully returns a numerical value: -0.97336.

So, why does the Sum function claim the series doesn't converge, but HurwitzZeta, which should be equivalent according to Mathematica's own symbolic computation, computes a numerical value without issue? Can anyone shed some light on this discrepancy or at least on what I am missing?

I've come across an issue while using Wolfram Mathematica that I don't quite understand.

Consider the following symbolic computation:

Clear[n, y, x]; Sum[1/(n + y)^x, {n, 0, Infinity}]

Mathematica returns: "HurwitzZeta[x, y]"

However, when I plug in specific values (x = 1/3, y = 1) to evaluate the sum:

x = 1/3; y = 1; Sum[1/(n + y)^x, {n, 0, Infinity}]

I get an error message: "Sum::div: Sum does not converge."

What confuses me is when I compute HurwitzZeta[1/3, 1] // N, it successfully returns a numerical value:

So, why does the Sum function claim the series doesn't converge, but HurwitzZeta, which should be equivalent according to Mathematica's own symbolic computation, computes a numerical value without issue? Can anyone shed some light on this discrepancy or at least on what I am missing?

I've come across an issue while using Wolfram Mathematica that I don't quite understand.

Consider the following symbolic computation:

Clear[n, y, x]; Sum[1/(n + y)^x, {n, 0, Infinity}]

Mathematica returns: "HurwitzZeta[x, y]"

However, when I plug in specific values (x = 1/3, y = 1) to evaluate the sum:

x = 1/3; y = 1; Sum[1/(n + y)^x, {n, 0, Infinity}]

I get an error message: "Sum::div: Sum does not converge."

What confuses me is when I compute HurwitzZeta[1/3, 1] // N, it successfully returns a numerical value: 1.082409227768647*10^18635.

So, why does the Sum function claim the series doesn't converge, but HurwitzZeta, which should be equivalent according to Mathematica's own symbolic computation, computes a numerical value without issue? Can anyone shed some light on this discrepancy or at least on what I am missing?