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  • $\begingroup$ As far as I know MA does not have incomplete Bessel functions. $\endgroup$ Commented Jun 23, 2024 at 8:13
  • $\begingroup$ How do you want to verify it? Numerically? As far as I can see your manipulation of the integral is correct so you have already proved it by hand. $\endgroup$ Commented Jun 23, 2024 at 10:10
  • $\begingroup$ People here generally like users to post code as copyable Mathematica code as well as images or TeX, so they can copy-paste it. It makes it convenient for them and more likely you will get someone to help you. You may find the meta Q&A, How to copy code from Mathematica so it looks good on this site, helpful $\endgroup$ Commented Jun 23, 2024 at 14:37