Abstract
The problem of finding the exact analytical closed-form solution of some families of transcendental equations, which describe two different physical phenomenon, thermionic emission and electrical conductivity in semiconductors, is studied, in some detail, by the Special Trans Functions Theory (STFT). The mathematical genesis of the analytical closed-form solution is presented, and the structure of the theoretical derivation, proofs and numerical results confirm the validity and base principle of the STFT. Undoubtedly, the proposed analytical approach implies the qualitative improvement of the conventional analytical and numerical methods.
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