  The deduction from solar flare X-ray photon spectroscopic data of the energy
dependent model-independent spectral index is considered as an inverse problem.
Using the well developed regularization approach we analyze the energy
dependency of spectral index for a high resolution energy spectrum provided by
Ramaty High Energy Solar Spectroscopic Imager (RHESSI). The regularization
technique produces much smoother derivatives while avoiding additional errors
typical of finite differences. It is shown that observations imply a spectral
index varying significantly with energy, in a way that also varies with time as
the flare progresses. The implications of these findings are discussed in the
solar flare context.
