```
using Plots
using SpecialFunctions
# using Elliptic
K = ellipk # Computes Complete Elliptic Integral of 1st kind K(m)
E = ellipe # Computes Complete Elliptic Integral of 2nd kind E(m)
psi0(k) = (K(k) - E(k)) / k
@show psi0(1e-8) # psi0(1.0e-8) = 0.7853981909278218
x = range(1e-5, 0.1, length=1000)
y = psi0
plot(x, y; label = :none)
```

The results are the same whether I use `SpecialFunctions`

or `Elliptic`

Now, from Wikipedia,

We neglect here the higher terms for `k`

approaching zero (by cropping screenshot )

Thus, for small k

`(K(k) - E(k)) / k ≈ k * π / 4 `

which tends to zero with `k`

tending to zero.

Not to `0.785...`