On the quantum differentiation of smooth real-valued functions
Résumé
Calculating the value of $C^{k\in\{1,\infty\}}$ class of smoothness real-valued function's derivative in point of $\mathbb{R}^+$ in radius of convergence of its Taylor polynomial (or series), applying an analog of Newton's binomial theorem and $q$-difference operator. $(P,q)$-power difference introduced in section 5. Additionally, by means of Newton's interpolation formula, the discrete analog of Taylor series, interpolation using $q$-difference and $p,q$-power difference is shown.
Mots clés
Calculus
Euler number
Mathematical Series
Monomial
Exponentiation
Exponential function
Numerical analysis
Newton's Binomial Theorem
Polynomial
Power function
Mathematical analysis
Number theory
Mathematics
Algebra
Power series (mathematics)
Binomial coefficient
Central Finite difference
Classical Analysis and ODEs
Numercal methods
Qunatum calculus
q-derivative
Jackson derivative
Discrete Mathematics
Quantum calculus
Analysis of PDEs
General Mathematics
q-difference
Time Scale Calculus
Quantum algebra
Quantum difference
Power quantum calculus
Series representation
Taylor's polynomial
Taylor's formula
Analytic function
Series Expansion
Taylor's series
Taylor's theorem
Maclaurin Series
Polynomial expansion
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On the quantum differentiation of smooth real-valued functions.pdf (180.36 Ko)
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