Solution to Sum of Exponential Squared Series

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The discussion revolves around finding a solution for the series \(\sum_{n=0}^\infty \left(\frac{x^n}{n!}\right)^2\). It is noted that the solution involves the Bessel function, specifically expressed as \(\sum_{k=0}^\infty \frac{x^{2k}}{k!(k+n)!}=x^{-n}I_n(2x)\). Participants reference the Modified Bessel Function of the First Kind for further understanding. The conversation highlights the complexity of the series and the need for advanced mathematical concepts to solve it. This topic emphasizes the intersection of exponential functions and special functions in mathematical series.
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I know:

\sum_{n=0}^\infty \frac{x^n}{n!}=e^x

However, is there a similar solution for:

\sum_{n=0}^\infty \left(\frac{x^n}{n!}\right)^2Thanks in advance; I'm not very good at this kind of maths (I teach statistics :devil:), and I've been struggling with this one for a while.
 
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