In this paper, we introduce a new function which is defined by replacing polynomials into polynomial factorials in the expansion of exponential function denoted by e~((k))e~((1)) entitled as extorial function, an original and unique contribution. Required identities involving difference operators with factorials are enumerated. And these identities are applied to obtain solutions of difference and discrete partial difference equation for heat flows and current flows in RL circuit. Numerical verifications validating the above results are included.
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