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Explicit Form of the Faulhaber Polynomials
The College Mathematics Journal, 2015Hersh recently showed that the Faulhaber polynomials, related to sums of consecutive powers, can be expressed as even or odd polynomials in the variable offset by one-half.
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Explicit Form of the Time Operator of a Gaussian Stationary Process
International Journal of Theoretical Physics, 2004A semigroup \(\{V_t\}_{t\in I}\) of isometries on a Hilbert space is called the time operator of a self-adjoint operator \((T,\mathcal D(T))\), if \(TV_t =V_t T+t V_t\) holds on \(\mathcal D(T)\) for all \(t\in I\). The author constructs the time operator for discrete time stationary Gaussian processes.
Z. Suchanecki, Z. Suchanecki
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A low complexity explicit rational centered form
Computing, 1985A centered form of very low complexity is defined for rational functions. Some numerical examples are calculated.
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Explicit/implicit partitioning and a new explicit form of the generalized alpha method
Communications in Numerical Methods in Engineering, 2003Abstractabstract Most finite element packages use the Newmark algorithm for time integration of structural dynamics. Various algorithms have been proposed to better optimize the high frequency dissipation of this algorithm. Hulbert and Chung proposed both implicit and explicit forms of the generalized alpha method.
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On the explicit form of $n$-group operations
Publicationes Mathematicae Debrecen, 2022openaire +2 more sources
Explicit closed forms for parametric integrals
International Journal of Mathematical Education in Science and Technology, 2004Closed forms are computed for parametric integrals, generally using induction formulas. It is shown that these integrals can be core activities, mixing hand-work, computations with a computer algebra system and experimental mathematics with an interactive website.
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Explicit forms for certain Hermite approximations
BIT, 1973The Hermite polynomial approximation in which function values and the first few derivatives of a given function are matched at two points is given in an explicit form and an error term is deduced. These results are extended to two dimensions.
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An explicit form of the differential equationsy″=q(t)y with periodic solutions
Annali Di Matematica Pura Ed Applicata, 1970F Neuman, Neuman F
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