In BCS theory, the superconducting gap is given by solving at different temperatures the integral
$$\frac{1}{N(0)V}=\int_0^{\hbar\omega_c}\frac{\tanh\frac{1}{2}\beta(\xi^2+\Delta^2)^{1/2}}{(\xi^2+\Delta^2)^{1/2}}$$
In textbooks like Tinkham (2nd edition, page 63) and Phillips (Advanced Solid State Physics, page 246) you can find approximate formulas for certain temperature ranges (typically $T\approx T_C$).

In some other references, such as [here][1] and [here][2] (for the latter, I couldn't find the arxiv version, sorry), it is mentioned an interpolation formula valid in the whole temperature range, that is
$$ \Delta(T)=\Delta_0\tanh (k\sqrt{\frac{T_{C}-T}{T}})$$
with $k=1.74$ or $k=2.2$.

Is there someone who can link a reference to this formula, and how it is obtained?


  [1]: https://books.google.it/books?id=qC_rCAAAQBAJ&pg=PA47&lpg=PA47&dq=interpolation%20formula%20superconducting%20gap%20parameter&source=bl&ots=s9XRWE19GK&sig=ItJusJbZmbq_NwHeOyFgTG8BtXk&hl=it&sa=X&ei=IHyVVZGsHIKCzAOooZOQAw&ved=0CCcQ6AEwATgK#v=onepage&q=interpolation%20formula%20superconducting%20gap%20parameter&f=false
  [2]: http://www.nature.com/nmat/journal/v10/n11/full/nmat3116.html