Relationship between partial and specific enthalpy

When the following summation is written out with the abbreviation 5 = d/dx, it looks like 

In the thermodynamics of mixtures [3.1], page 114, it can be shown, that for specific partial quantities of state the following relationship is valid 

All the integrals on the right hand side disappear when m n, yielding (3.248). In order to show that this applies, we write (3.245) for the eigenvalues f3m and /  

Multiplication of the first equation with ipn and of the second with ipm gives 

Subtraction of both equations and integration between the limits r+ = 0 and r+ = 1 yields 

---