Error when using \begin{split} and \end{split} to align equation

Question

The following code gives me exactly what I need as displayed in the image. It's however displaying error messages when I run. How do I get rid of the errors displayed. Below is the code and equation.

\documentclass{article}
\usepackage{amsmath}
\begin{document}
 \begin{equation*}
\begin{split}
{\alpha}^{(k+1)}&=\frac{-n}{\sum\limits_{i=1}^{m}\ln\left( 
e^{{\lambda}^{(k)}/x_i^{\beta^{(k)}}}-1\right)-2\sum\limits_{i=1}^{m} \cfrac{\left( 
e^{{\lambda}^{(k)}/x_i^{\beta^{(k)}}}-1\right)^{\alpha^{(k+1)}}\ln\left( 
e^{{\lambda}^{(k)}/x_i^{\beta^{(k)}}}-1\right)}{\left( 
e^{{\lambda}^{(k)}/x_i^{\beta^{(k)}}}-1\right)^{\alpha^{(k+1)}}+1}  \\&+\sum\limits_{i=1}^{m} 
{R_i} C(x_i;{\alpha}^{(k)},{\beta}^{(k)},{\lambda}^{(k)} )        }
 \end{split}
\end{equation*}
\end{document}

---

! Missing } inserted.
<inserted text> 
                }
l.12  \end{split}
                 
? 

Answer 1

After correcting your code, I also changed equation*/split environments to align*. The code is structured a little bit to see better what's happening after compilation and how parts of the code correspond to the outcome. You could also think about using intermediate terms as the equation is too long to fit a page

\documentclass{article}
\usepackage{mathtools}

\begin{document}
\begin{align*}
    \alpha^{(k+1)} &= \frac{-n}{A - 2B + C}
    \intertext{with}
     A &= \sum\limits_{i=1}^{m}
             \ln\Bigl(
                 e^{\lambda^{(k)}/x_i^{\beta^{(k)}}} - 1
             \Bigr) \\
     B &= \sum\limits_{i=1}^{m}
             \cfrac{
                 \Bigl(
                     e^{{\lambda}^{(k)}/x_i^{\beta^{(k)}}} - 1
                 \Bigr)^{\alpha^{(k+1)}}
                 \ln \Bigl(
                     e^{{\lambda}^{(k)}/x_i^{\beta^{(k)}}} - 1
                 \Bigr)
             }{
                 \Bigl(
                     e^{{\lambda}^{(k)}/x_i^{\beta^{(k)}}} - 1
                 \Bigr)^{\alpha^{(k+1)}} + 1
             } \\
     C &= \sum\limits_{i=1}^{m}
             R_i
             C\Bigl(
                x_i;\alpha^{(k)},\beta^{(k)},\lambda^{(k)}
             \Bigr)
\end{align*}
\end{document}

Answer 2

I would like to suggest you simplify the notation along the following lines. Actually, since your code contains some syntax errors, I couldn't decide which of the following two equations for \alpha^{(k+1)} is correct.

\documentclass{article}
\usepackage{mathtools} % for \coloneqq macro
\begin{document}
\noindent
Put $U_i\coloneqq\exp\bigl( \lambda^{(k)}/x_i^{\beta^{(k)}} \bigr) -1$ 
and $V_i\coloneqq U_i^{\alpha^{(k+1)}}$. 
Then either
\begin{equation*}
\alpha^{(k+1)}
=-n\bigg/ \biggl(\,
    \sum_{i=1}^{m}\ln U_i 
  -2\sum_{i=1}^{m} \frac{V_i\ln U_i}{V_i+1}\biggr)
   +\sum_{i=1}^{m} R_i C\bigl(x_i;\alpha^{(k)},\beta^{(k)},\lambda^{(k)}\bigr)\,.
\end{equation*}
or
\begin{equation*}
\alpha^{(k+1)}
=-n\bigg/ \biggl(\,
    \sum_{i=1}^{m}\ln U_i 
  -2\sum_{i=1}^{m} \frac{V_i\ln U_i}{V_i+1}
   +\sum_{i=1}^{m} R_i C\bigl(x_i;\alpha^{(k)},\beta^{(k)},\lambda^{(k)}\bigr) \biggr) \,.
\end{equation*}
\end{document}

Answer 3

I got the same error when using mathjax with nested equation containing spaces..

Error Instance raising \begin{aligned} ended with \end{split}

$$\begin{aligned}
& \,\,\,\, -   {\partial \over \partial m}  \log \sum_z q_e(z|x) q_r(y|z) 
\\

&= \sum_z  q_w(z|x)  \left[ \begin{aligned}
\log {q_e(z|x) q_r(y|z)  \over q_w(z|x)} 
  {\partial \over \partial m}  \log q_w(z|x)  \\
 +  {\partial \over \partial m}  \log q_e(z|x) q_r(y|z) \\
 - {\partial \over \partial m}\log q_w(z|x)  \end{aligned} 
\right]  -   {\partial \over \partial m}  l  \\

&= \sum_z {\partial \over \partial m}\left[ 
 q_w(z|x) \log {q_e(z|x) q_r(y|z)  \over q_w(z|x)} 
    \right ]
   -   {\partial \over \partial m}  l  \\
&= {\partial \over \partial m} \sum_z \left[ 
 q_w(z|x) \log {q_e(z|x) q_r(y|z)  \over q_w(z|x)} 
    \right ]
   -   {\partial \over \partial m}  l  \\
-{\partial \over \partial m} D_{KL} &= {\partial \over \partial m} ELBO
   -   {\partial \over \partial m}  l 
\end{aligned}$$

Removing all newlines would remove the error, yielding

$$\begin{aligned}
& \,\,\,\, -   {\partial \over \partial m}  \log \sum_z q_e(z|x) q_r(y|z) 
\\
&= \sum_z  q_w(z|x)  \left[ \begin{aligned}
\log {q_e(z|x) q_r(y|z)  \over q_w(z|x)} 
  {\partial \over \partial m}  \log q_w(z|x)  \\
 +  {\partial \over \partial m}  \log q_e(z|x) q_r(y|z) \\
 - {\partial \over \partial m}\log q_w(z|x)  \end{aligned} 
\right]  -   {\partial \over \partial m}  l  \\
&= \sum_z {\partial \over \partial m} \left[ 
 q_w(z|x) \log {q_e(z|x) q_r(y|z)  \over q_w(z|x)} 
    \right ] -   {\partial \over \partial m}  l  \\
&= {\partial \over \partial m} \sum_z \left[ 
 q_w(z|x) \log {q_e(z|x) q_r(y|z)  \over q_w(z|x)} 
    \right ]  -   {\partial \over \partial m}  l  \\
-{\partial \over \partial m} D_{KL} &= {\partial \over \partial m} ELBO
   -   {\partial \over \partial m}  l 
\end{aligned}$$

Not sure which exact newline causing the problem, but maybe related to mathjax inserting {split} environment