BibSonomy bookmarks for /user/kolosov_petro/Binomialhttps://www.bibsonomy.org/user/kolosov_petro/BinomialBibSonomy RSS Feed for /user/kolosov_petro/Binomial[1705.02516] On the quantum differentiation of smooth real-valued functionsCalculating 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.https://arxiv.org/abs/1705.02516kolosov_petro2017-09-09T02:23:33+02:00Binomial Derivative Double Exponential Finite Jackson Monomial Newton's Pascalâ€™s Polynomial Power Series Sum Taylor's Theorem algebra analysis arxiv calculus coefficient derivative difference differential differentiation divided equations expansion finite formula function high interpolation math mathematics maths ode open order partial pde polynomial power preprint q-calculus q-derivative q-difference quantum real science series smooth theorem triangle <span itemprop="description">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.</span>