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\documentclass{article}

\usepackage{amsmath}

\begin{document}
$$\hat{\alpha_1}=\dfrac{\sum_{i=1}^{n}w_i\cos(y_i-\beta_i\hat{X_i})}{\sum_{i=1}^{n}w_i}$$


$$\rightarrow\dfrac{1}{(2\pi)^n} \left[\dfrac{1}{I_0(\lambda\rho)}\right]^n \exp \sum_{i=1}^{n}\lambda \rho \cos(x_i -X_i)\dfrac{1}{\prod_{i=1}^{n}(c-\eta_1 \cos(y_i-\beta_i X_i)-\eta_2\sin(y_i-\beta_i X_i))}$$

\end{document}
bmv
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Rita ana
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    Rita, please, complete your code with all the necessary code between the \documentclass and the \end{document}. I compiled your equations here and I could see no "problem". So please, complete the code and clarify what you mean by "problem". – Phelype Oleinik Feb 15 '18 at 14:07
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    Make your example start with \documentclass end with \end{document} and not use $$ – David Carlisle Feb 15 '18 at 14:08
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    While you wait for an answer to this question, can you go back to your previous ones and look if the answers solve your problems and accept them, if they do? – samcarter_is_at_topanswers.xyz Feb 15 '18 at 14:27
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    Dear @Rita ana, so far you should learn something from received comments and answers. (i) tell us, why you newer provides small but complete document beginning with \documentclass[<opions, if any>]{<used document class>} followed by loading packages, which are relevant to your problem, than begin{document} ... code of your problem ... \end{document} as you can see in all received answers, which demonstrate your problem; (ii) why not consider given advises to change used syntax in typing of math expression; (iii) why so far you not accept any of received answers. are they all worth less? – Zarko Feb 15 '18 at 14:51

1 Answers1

1

You should use \limits for placing indices right under and above the sum and the product sign. (If it was your question)

Instead of $$...$$ you should use \[...\], see Why is \[ ... \] preferable to $$ ... $$?

Also, I changed \hat{\alpha_1} to \hat{\alpha}_1, then the hat will be placed only above \alpha.

\documentclass{article}

\usepackage{amsmath}

\begin{document}
\[\hat{\alpha}_1=\dfrac{\sum\limits_{i=1}^{n}w_i\cos(y_i-\beta_i\hat{X}_i)}{\sum\limits_{i=1}^{n}w_i}\]

\[\rightarrow\dfrac{1}{(2\pi)^n} \left[\dfrac{1}{I_0(\lambda\rho)}\right]^n \exp \sum\limits_{i=1}^{n}\lambda \rho \cos(x_i -X_i)\dfrac{1}{\prod\limits_{i=1}^{n}(c-\eta_1 \cos(y_i-\beta_i X_i)-\eta_2\sin(y_i-\beta_i X_i))}\]

\end{document}
bmv
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