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As the title shows, I'm looking to find the coefficient of $x^n$ in $$\sinh^a x\cdot \cosh^b x \cdot e^{cx}$$ at $x=0$, as a follow-up to this question. Expressing the hyperbolic functions in terms of $e^x$ and $e^{-x}$ doesn't do much to simplify the question.

Maybe I'm missing something, but perhaps this closed form is too complicated to be found?

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  • $\begingroup$ Cauchy products? $\endgroup$ – Simply Beautiful Art Jun 10 '17 at 17:16
  • $\begingroup$ $a,b\in\mathbb N$? $\endgroup$ – Simply Beautiful Art Jun 10 '17 at 17:25
  • $\begingroup$ Sorry, the notification wasn't updated properly. Yes, $a, b$ are natural numbers, starting from $0$. $\endgroup$ – programmer101 Jun 10 '17 at 17:28

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