Series[ Exp[Sin [Sqrt[1 + x^2]]], {x, Infinity, 1}]
E^Sin[Sqrt[1 + x^2]]

Output is same as input whereas I want this answer...

E^Sin[1/(2 x) + x + ...]

WITHOUT having to manually expand the square root separately. I thinking of a long expression where many Exponentials and Sines and square roots are present in that expression.

  • $\begingroup$ Try D[Exp[Sin[Sqrt[1+x^2]]]]/.x->Infinity and see the result obtained. $\endgroup$ – Nasser Mar 6 '17 at 8:11

Try this:

MapAt[Normal[Series[#, {x, \[Infinity], 1}]] &, expr, {2, 1}]

(*  E^Sin[1/(2 x) + x]  *)

Have fun!


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