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Calculating the value of Ck ∈ {1, ∞} class of smoothness real-valued function's derivative in point of 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.
Report on the paper "ROM for non-linear conservative law" for group meeting
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Fortgeschrittenenpraktikum Astronomie Hausarbeit an der Universitäts-Sternwarte München (LMU).
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In this paper, we derive and prove, by means of Binomial theorem and Faulhaber's formula, the following identity between $m$-order polynomials in \(T\) \(\sum_{k=1}^{\ell}\sum_{j=0}^m A_{m,j}k^j(T-k)^j=\sum_{k=0}^{m}(-1)^{m-k}U_m(\ell,k)\cdot T^k=T^{2m+1}, \ \ell=T\in\mathbb{N}.\)
homework 4m
Lagrange's Theorem
Az egész együtthatós polinomok Q és Z feletti felbontásainak kapcsolatáról szóló tétel bizonyítása. (Az SZTE matematika alapszak Algebra és számelmélet (MBNK13) kurzusához házi feladat.)