Published May 30, 2017 | Version v1
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On the quantum differentiation of smooth real-valued functions

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Abstract. 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.

MSC 2010: 26A24, 05A30, 41A58

arXiv:1705.02516

Notes

12 pages, 6 figures, arXiv:1705.02516

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References

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Subjects

Mathematics
1
Math
2
Maths
3
Science
4
Algebra
5
Number theory
6
Numerical analysis
7
Mathematical analysis
8
Functional analysis
9
STEM
10
Numercal methods
11
Classical Analysis and ODEs
12
Analysis of PDEs
13
General Mathematics
14
Discrete Mathematics
15
Applied Mathematics
16
Calculus of variations
17