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?