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Carl Woll
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I think the behavior described is a bug, and I think it is related to the new enhanced support of Assumptions in Limit. In M11.1 we have:

Series[1 + (1 + Sqrt[1/(1-x)]) Sqrt[1/(1-x)] , {x, 1, 3}] //TeXForm 

$-\frac{1}{x-1}+\frac{i}{\sqrt{x-1}}+1+O\left((x-1)^{7/2}\right)$

Note how the terms are powers of $x-1$. If we tell M11.1 that $x<1$, we get:

Series[1 + (1 + Sqrt[1/(1-x)]) Sqrt[1/(1-x)], {x, 1, 3}, Assumptions->x<1] //TeXForm 

$-\frac{1}{x-1}+\frac{i}{\sqrt{x-1}}+1+O\left((x-1)^{7/2}\right)$

which is the same as before, even though we might wish to have a power series in $1-x$. Now, in M11.2, we have:

Series[1 + (1 + Sqrt[1/(1-x)]) Sqrt[1/(1-x)], {x, 1, 3}, Assumptions->x>1] //TeXForm 

$-\frac{1}{x-1}+\frac{i}{\sqrt{x-1}}+1+O\left((x-1)^{7/2}\right)$

Series[1 + (1 + Sqrt[1/(1-x)]) Sqrt[1/(1-x)], {x, 1, 3}, Assumptions->x<1] //TeXForm 

$\left(\frac{1}{\sqrt{1-x}}+\frac{1}{1-x}+1\right)+O\left((x-1)^4\right)$

Notice that the Assumptions -> x>1 version returns what M11.1 did, while the Assumptions -> x<1 version has the issues described in the OP. In particular, we see that Series is trying to create a power series in $1-x$ (note the Sqrt[1-x] and 1/(1-x) terms), but the overall SeriesData object is a power series in $x-1$, and so problems arise.

Until these issues are worked out, it might make sense to use Assumptions->x>1 in your code.

I think the behavior described is a bug, and I think it is related to the new enhanced support of Assumptions in Limit. In M11.1 we have:

Series[1 + (1 + Sqrt[1/(1-x)]) Sqrt[1/(1-x)] , {x, 1, 3}] //TeXForm 

$-\frac{1}{x-1}+\frac{i}{\sqrt{x-1}}+1+O\left((x-1)^{7/2}\right)$

Note how the terms are powers of $x-1$. If we tell M11.1 that $x<1$, we get:

Series[1 + (1 + Sqrt[1/(1-x)]) Sqrt[1/(1-x)], {x, 1, 3}, Assumptions->x<1] //TeXForm 

$-\frac{1}{x-1}+\frac{i}{\sqrt{x-1}}+1+O\left((x-1)^{7/2}\right)$

which is the same as before, even though we might wish to have a power series in $1-x$. Now, in M11.2, we have:

Series[1 + (1 + Sqrt[1/(1-x)]) Sqrt[1/(1-x)], {x, 1, 3}, Assumptions->x>1] //TeXForm 

$-\frac{1}{x-1}+\frac{i}{\sqrt{x-1}}+1+O\left((x-1)^{7/2}\right)$

Series[1 + (1 + Sqrt[1/(1-x)]) Sqrt[1/(1-x)], {x, 1, 3}, Assumptions->x<1] //TeXForm 

$\left(\frac{1}{\sqrt{1-x}}+\frac{1}{1-x}+1\right)+O\left((x-1)^4\right)$

Notice that the Assumptions -> x>1 version returns what M11.1 did, while the Assumptions -> x<1 version has the issues described in the OP. Until these issues are worked out, it might make sense to use Assumptions->x>1 in your code.

I think the behavior described is a bug, and I think it is related to the new enhanced support of Assumptions in Limit. In M11.1 we have:

Series[1 + (1 + Sqrt[1/(1-x)]) Sqrt[1/(1-x)] , {x, 1, 3}] //TeXForm 

$-\frac{1}{x-1}+\frac{i}{\sqrt{x-1}}+1+O\left((x-1)^{7/2}\right)$

Note how the terms are powers of $x-1$. If we tell M11.1 that $x<1$, we get:

Series[1 + (1 + Sqrt[1/(1-x)]) Sqrt[1/(1-x)], {x, 1, 3}, Assumptions->x<1] //TeXForm 

$-\frac{1}{x-1}+\frac{i}{\sqrt{x-1}}+1+O\left((x-1)^{7/2}\right)$

which is the same as before, even though we might wish to have a power series in $1-x$. Now, in M11.2, we have:

Series[1 + (1 + Sqrt[1/(1-x)]) Sqrt[1/(1-x)], {x, 1, 3}, Assumptions->x>1] //TeXForm 

$-\frac{1}{x-1}+\frac{i}{\sqrt{x-1}}+1+O\left((x-1)^{7/2}\right)$

Series[1 + (1 + Sqrt[1/(1-x)]) Sqrt[1/(1-x)], {x, 1, 3}, Assumptions->x<1] //TeXForm 

$\left(\frac{1}{\sqrt{1-x}}+\frac{1}{1-x}+1\right)+O\left((x-1)^4\right)$

Notice that the Assumptions -> x>1 version returns what M11.1 did, while the Assumptions -> x<1 version has the issues described in the OP. In particular, we see that Series is trying to create a power series in $1-x$ (note the Sqrt[1-x] and 1/(1-x) terms), but the overall SeriesData object is a power series in $x-1$, and so problems arise.

Until these issues are worked out, it might make sense to use Assumptions->x>1 in your code.

Source Link
Carl Woll
  • 132.7k
  • 6
  • 253
  • 366

I think the behavior described is a bug, and I think it is related to the new enhanced support of Assumptions in Limit. In M11.1 we have:

Series[1 + (1 + Sqrt[1/(1-x)]) Sqrt[1/(1-x)] , {x, 1, 3}] //TeXForm 

$-\frac{1}{x-1}+\frac{i}{\sqrt{x-1}}+1+O\left((x-1)^{7/2}\right)$

Note how the terms are powers of $x-1$. If we tell M11.1 that $x<1$, we get:

Series[1 + (1 + Sqrt[1/(1-x)]) Sqrt[1/(1-x)], {x, 1, 3}, Assumptions->x<1] //TeXForm 

$-\frac{1}{x-1}+\frac{i}{\sqrt{x-1}}+1+O\left((x-1)^{7/2}\right)$

which is the same as before, even though we might wish to have a power series in $1-x$. Now, in M11.2, we have:

Series[1 + (1 + Sqrt[1/(1-x)]) Sqrt[1/(1-x)], {x, 1, 3}, Assumptions->x>1] //TeXForm 

$-\frac{1}{x-1}+\frac{i}{\sqrt{x-1}}+1+O\left((x-1)^{7/2}\right)$

Series[1 + (1 + Sqrt[1/(1-x)]) Sqrt[1/(1-x)], {x, 1, 3}, Assumptions->x<1] //TeXForm 

$\left(\frac{1}{\sqrt{1-x}}+\frac{1}{1-x}+1\right)+O\left((x-1)^4\right)$

Notice that the Assumptions -> x>1 version returns what M11.1 did, while the Assumptions -> x<1 version has the issues described in the OP. Until these issues are worked out, it might make sense to use Assumptions->x>1 in your code.