We have tried to solve this problem.
Let do it one more - help me please to find not numeric (see please the picture and the Mathcad 15 sheet in attach) but symbolic value of this constant! As any closed (implicit) formula - as here
From your integral for L we have that a*sinh(X/a) = L/2 ...(1)
If X is known and L is specified as a multiple of X then the only unknown is ‘a’. Unfortunately, there is no known analytical solution to (1) that I’m aware of (certainly not in terms of elementary functions), which means that any attempt to find a symbolic expression for your catenary constant is doomed to failure!
Alan
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