Derivatives of the Grneisen and Einstein Functions

The function CO(8/T) is frequently referred to as the Griineisen fu nction. This fun ction is approximately unity for T P 8, which indicates that at high temperatures electrical resistivity increases linearly with temperature. At very low temperatures where T ~ 8, the Griineisen function can be expressed approximately by CO(8/T) = B (T/8)\ which indicates that at very low temperatures electrical resistivity increases with the fifth power of temperature. For various calculations, the successive derivatives of the electrical resistivity function may be needed_ This req uires a knowledge of the derivatives of the Griineisen function. Also, it may be possible to make further refinem ents in the electrical resistivity expression by expanding the resistivity fun ction in the derivatives of the Griineisen function. It was observed that the derivatives of the Griine isen function contain th e Einstein function and its successive derivatives. The objective of this writing is to obtain expressions for the successive derivatives of the Griineisen and the Einstein fun c tions.