Umbral operator techniques are applied to q-calculus to formally derive q-Gaussian and q-Fresnel integral identities and q-trigonometric functions, with limited rigorous justification.
Umbral Calculus, a Different Mathematical Language
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abstract
This thesis is intended to provide an account of the theory and applications of Operational Methods that allow the "translation" of the theory of special functions and polynomials into a "different" mathematical language. The language we are referring to is that of symbolic methods, largely based on a formalism of umbral type which provides a tremendous simplification of the derivation of the associated properties. The strategy we will follow is that of establishing the rules to replace higher trascendental functions in terms of elementary functions and to take advantage from such a recasting.
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2019 1verdicts
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Can Umbral and $q$-calculus be merged?
Umbral operator techniques are applied to q-calculus to formally derive q-Gaussian and q-Fresnel integral identities and q-trigonometric functions, with limited rigorous justification.