3 Routine clean-up

# "Division by a Series with no Coefficients in..." Error in Taylor Expansion?when simplifying a series expression

I have the following function which I call FF[q_,y_,u_] and this function is well known to have a reasonable Taylor expansion in all three variables. For example, there are no negative powers of $$q$$, expanding $$u$$ around 1, there is at worst a second order pole $$(u-1)^{-2}$$, etc. However, when I try to implement and manipulate this expansion in Mathematica, I get very weird results. For example, when I try to run the following

FF[q_, y_, u_] := (y^(-1))*(((1 - u)*(1 - (1/u))/((1 - (y)*(1/u))*(1 - u*y)))^(-1))*((QPochhammer[y*u, q]* QPochhammer[y^(-1)*u^(-1), q]*QPochhammer[y*u^(-1), q]* QPochhammer[y^(-1)*u, q])/((QPochhammer[u, q]^2)*(QPochhammer[1/u, q])^2)); FullSimplify[ Series[FF[q, y, u], {u, 1, 2}, {q, 0, 1}, {y, 0, 1}]]

FF[q_, y_, u_] :=
(y^(-1))*(((1 - u)*(1 - (1/u))/((1 - (y)*(1/u))*(1 - u*y)))^(-1))*
((QPochhammer[y*u, q]*QPochhammer[y^(-1)*u^(-1), q]*
QPochhammer[y*u^(-1), q]*QPochhammer[y^(-1)*u, q])/
((QPochhammer[u, q]^2)*(QPochhammer[1/u, q])^2));
FullSimplify[Series[FF[q, y, u], {u, 1, 2}, {q, 0, 1}, {y, 0, 1}]]


I get the mysterious error "division by series with no coefficients in $$\mathcal{O}(q^{87})$$"

"division by series with no coefficients in $$\mathcal{O}(q^{87})$$"

or something crazy. I've

I've tried changing the order in which I expand and, but I still get this error. I get the same error when I try to isolate the coefficient of $$(u-1)^{0}$$:

SeriesCoefficient[FF[q, y, u], {u, 1, 0}] FullSimplify[Series[%, {q, 0, 2}, {y, 0, 2}]]

SeriesCoefficient[FF[q, y, u], {u, 1, 0}]
FullSimplify[Series[%, {q, 0, 2}, {y, 0, 2}]]


My question is, what exactly is going on here? Is it something I'm doing, or a Mathematica glitch with regards to this specific function? And more generally, are there oddities one has to keep in mind when naively doing this series mongeringmunging in Mathematica?

# "Division by a Series with no Coefficients in..." Error in Taylor Expansion?

I have the following function which I call FF[q_,y_,u_] and this function is well known to have a reasonable Taylor expansion in all three variables. For example, there are no negative powers of $$q$$, expanding $$u$$ around 1, there is at worst a second order pole $$(u-1)^{-2}$$, etc. However, when I try to implement and manipulate this expansion in Mathematica, I get very weird results. For example, when I try to run the following

FF[q_, y_, u_] := (y^(-1))*(((1 - u)*(1 - (1/u))/((1 - (y)*(1/u))*(1 - u*y)))^(-1))*((QPochhammer[y*u, q]* QPochhammer[y^(-1)*u^(-1), q]*QPochhammer[y*u^(-1), q]* QPochhammer[y^(-1)*u, q])/((QPochhammer[u, q]^2)*(QPochhammer[1/u, q])^2)); FullSimplify[ Series[FF[q, y, u], {u, 1, 2}, {q, 0, 1}, {y, 0, 1}]]

I get the mysterious error "division by series with no coefficients in $$\mathcal{O}(q^{87})$$" or something crazy. I've tried changing the order in which I expand and I still get this error. I get the same error when I try to isolate the coefficient of $$(u-1)^{0}$$:

SeriesCoefficient[FF[q, y, u], {u, 1, 0}] FullSimplify[Series[%, {q, 0, 2}, {y, 0, 2}]]

My question is, what exactly is going on here? Is it something I'm doing, or a Mathematica glitch with regards to this specific function? And more generally, are there oddities one has to keep in mind when naively doing this series mongering in Mathematica?

# Error when simplifying a series expression

I have the following function which I call FF[q_,y_,u_] and this function is well known to have a reasonable Taylor expansion in all three variables. For example, there are no negative powers of $$q$$, expanding $$u$$ around 1, there is at worst a second order pole $$(u-1)^{-2}$$, etc. However, when I try to implement and manipulate this expansion in Mathematica, I get very weird results. For example, when I try to run the following

FF[q_, y_, u_] :=
(y^(-1))*(((1 - u)*(1 - (1/u))/((1 - (y)*(1/u))*(1 - u*y)))^(-1))*
((QPochhammer[y*u, q]*QPochhammer[y^(-1)*u^(-1), q]*
QPochhammer[y*u^(-1), q]*QPochhammer[y^(-1)*u, q])/
((QPochhammer[u, q]^2)*(QPochhammer[1/u, q])^2));
FullSimplify[Series[FF[q, y, u], {u, 1, 2}, {q, 0, 1}, {y, 0, 1}]]


I get the mysterious error

"division by series with no coefficients in $$\mathcal{O}(q^{87})$$"

or something crazy.

I've tried changing the order in which I expand, but I still get this error. I get the same error when I try to isolate the coefficient of $$(u-1)^{0}$$:

SeriesCoefficient[FF[q, y, u], {u, 1, 0}]
FullSimplify[Series[%, {q, 0, 2}, {y, 0, 2}]]


My question is, what exactly is going on here? Is it something I'm doing, or a Mathematica glitch with regards to this specific function? And more generally, are there oddities one has to keep in mind when naively doing this series munging in Mathematica?

2 deleted 9 characters in body; edited title

# "Division by a Series with no Coefficients in..." Error in FourierTaylor Expansion?

I have the following function which I call F[q_FF[q_,y_,u_] and this function is well known to have a reasonable FourierTaylor expansion in all three variables. For example, there are no negative powers of $$q$$, expanding $$u$$ around 1, there is at worst a second order pole $$(u-1)^{-2}$$, etc. However, when I try to implement and manipulate this Fourier expansion in Mathematica, I get very weird results. For example, when I try to run the following

FF[q_, y_, u_] := (y^(-1))*(((1 - u)*(1 - (1/u))/((1 - (y)*(1/u))*(1 - u*y)))^(-1))*((QPochhammer[y*u, q]* QPochhammer[y^(-1)*u^(-1), q]*QPochhammer[y*u^(-1), q]* QPochhammer[y^(-1)*u, q])/((QPochhammer[u, q]^2)*(QPochhammer[1/u, q])^2)); FullSimplify[ Series[FF[q, y, u], {u, 1, 2}, {q, 0, 1}, {y, 0, 1}]]

I get the mysterious error "division by series with no coefficients in $$\mathcal{O}(q^{87})$$" or something crazy. I've tried changing the order in which I expand and I still get this error. I get the same error when I try to isolate the coefficient of $$(u-1)^{0}$$:

SeriesCoefficient[FF[q, y, u], {u, 1, 0}] FullSimplify[Series[%, {q, 0, 2}, {y, 0, 2}]]

My question is, what exactly is going on here? Is it something I'm doing, or a Mathematica glitch with regards to this specific function? And more generally, are there oddities one has to keep in mind when naively doing this series mongering in Mathematica?

# "Division by a Series with no Coefficients in..." Error in Fourier Expansion?

I have the following function which I call F[q_,y_,u_] and this function is well known to have a reasonable Fourier expansion in all three variables. For example, there are no negative powers of $$q$$, expanding $$u$$ around 1, there is at worst a second order pole $$(u-1)^{-2}$$, etc. However, when I try to implement and manipulate this Fourier expansion in Mathematica, I get very weird results. For example, when I try to run the following

FF[q_, y_, u_] := (y^(-1))*(((1 - u)*(1 - (1/u))/((1 - (y)*(1/u))*(1 - u*y)))^(-1))*((QPochhammer[y*u, q]* QPochhammer[y^(-1)*u^(-1), q]*QPochhammer[y*u^(-1), q]* QPochhammer[y^(-1)*u, q])/((QPochhammer[u, q]^2)*(QPochhammer[1/u, q])^2)); FullSimplify[ Series[FF[q, y, u], {u, 1, 2}, {q, 0, 1}, {y, 0, 1}]]

I get the mysterious error "division by series with no coefficients in $$\mathcal{O}(q^{87})$$" or something crazy. I've tried changing the order in which I expand and I still get this error. I get the same error when I try to isolate the coefficient of $$(u-1)^{0}$$:

SeriesCoefficient[FF[q, y, u], {u, 1, 0}] FullSimplify[Series[%, {q, 0, 2}, {y, 0, 2}]]

My question is, what exactly is going on here? Is it something I'm doing, or a Mathematica glitch with regards to this specific function? And more generally, are there oddities one has to keep in mind when naively doing this series mongering in Mathematica?

# "Division by a Series with no Coefficients in..." Error in Taylor Expansion?

I have the following function which I call FF[q_,y_,u_] and this function is well known to have a reasonable Taylor expansion in all three variables. For example, there are no negative powers of $$q$$, expanding $$u$$ around 1, there is at worst a second order pole $$(u-1)^{-2}$$, etc. However, when I try to implement and manipulate this expansion in Mathematica, I get very weird results. For example, when I try to run the following

FF[q_, y_, u_] := (y^(-1))*(((1 - u)*(1 - (1/u))/((1 - (y)*(1/u))*(1 - u*y)))^(-1))*((QPochhammer[y*u, q]* QPochhammer[y^(-1)*u^(-1), q]*QPochhammer[y*u^(-1), q]* QPochhammer[y^(-1)*u, q])/((QPochhammer[u, q]^2)*(QPochhammer[1/u, q])^2)); FullSimplify[ Series[FF[q, y, u], {u, 1, 2}, {q, 0, 1}, {y, 0, 1}]]

I get the mysterious error "division by series with no coefficients in $$\mathcal{O}(q^{87})$$" or something crazy. I've tried changing the order in which I expand and I still get this error. I get the same error when I try to isolate the coefficient of $$(u-1)^{0}$$:

SeriesCoefficient[FF[q, y, u], {u, 1, 0}] FullSimplify[Series[%, {q, 0, 2}, {y, 0, 2}]]

My question is, what exactly is going on here? Is it something I'm doing, or a Mathematica glitch with regards to this specific function? And more generally, are there oddities one has to keep in mind when naively doing this series mongering in Mathematica?

1

# "Division by a Series with no Coefficients in..." Error in Fourier Expansion?

I have the following function which I call F[q_,y_,u_] and this function is well known to have a reasonable Fourier expansion in all three variables. For example, there are no negative powers of $$q$$, expanding $$u$$ around 1, there is at worst a second order pole $$(u-1)^{-2}$$, etc. However, when I try to implement and manipulate this Fourier expansion in Mathematica, I get very weird results. For example, when I try to run the following

FF[q_, y_, u_] := (y^(-1))*(((1 - u)*(1 - (1/u))/((1 - (y)*(1/u))*(1 - u*y)))^(-1))*((QPochhammer[y*u, q]* QPochhammer[y^(-1)*u^(-1), q]*QPochhammer[y*u^(-1), q]* QPochhammer[y^(-1)*u, q])/((QPochhammer[u, q]^2)*(QPochhammer[1/u, q])^2)); FullSimplify[ Series[FF[q, y, u], {u, 1, 2}, {q, 0, 1}, {y, 0, 1}]]

I get the mysterious error "division by series with no coefficients in $$\mathcal{O}(q^{87})$$" or something crazy. I've tried changing the order in which I expand and I still get this error. I get the same error when I try to isolate the coefficient of $$(u-1)^{0}$$:

SeriesCoefficient[FF[q, y, u], {u, 1, 0}] FullSimplify[Series[%, {q, 0, 2}, {y, 0, 2}]]

My question is, what exactly is going on here? Is it something I'm doing, or a Mathematica glitch with regards to this specific function? And more generally, are there oddities one has to keep in mind when naively doing this series mongering in Mathematica?