#APL(NARS), 54 chars, 108 bytes

 {q←z×z←1.96⋄h←z×√(⍺×⍵÷n←⍺+⍵)+q÷4⋄(n+q)÷⍨(⍺+q÷2)+(-h)h}
test:

 f←{q←z×z←1.96⋄h←z×√(⍺×⍵÷n←⍺+⍵)+q÷4⋄(n+q)÷⍨(⍺+q÷2)+(-h)h}
 0 f 1
 0 0.7934567085 
 25 f 75
 0.17545094 0.3430464637 
 1 f 0
 0.2065432915 1