Best quadrature formulas on classes of differentiable periodic functions

1969 ◽  
Vol 6 (4) ◽  
pp. 740-744 ◽  
Author(s):  
N. E. Lushpai
Keyword(s):  
Quadrature Formulas ◽  
Periodic Functions

Best quadrature formulas for certain classes of periodic functions

1978 ◽  
Vol 24 (5) ◽  
pp. 853-857 ◽  
Author(s):  
A. A. Ligun
Keyword(s):  
Quadrature Formulas ◽  
Periodic Functions

scholarly journals Estimates of the error of interval quadrature formulas on some classes of differentiable functions

2020 ◽  
Vol 28 (1) ◽  
pp. 12
Author(s):  
V.P. Motornyi ◽  
D.A. Ovsyannikov
Keyword(s):  
Quadrature Formula ◽  
Modulus Of Continuity ◽  
Quadrature Formulas ◽  
Periodic Functions ◽  
Differentiable Functions ◽  
The Given

The exact value of error of interval quadrature formulas$$\int_0^{2\pi}f(t)dt -\frac{\pi}{nh}\sum_{k=0}^{n-1}\int_{-h}^hf(t+\frac {2k\pi}{n})dt = R_n(f;\vec{c_0};\vec{x_0};h)$$obtained for the classes $W^rH^{\omega} (r=1,2,...)$ of differentiable periodic functions for which the modulus of continuity of the  $r -$th derivative is majorized by the given modulus of continuity $\omega(t)$. This interval quadrature formula coincides with the rectangles formula for the Steklov functions $f_h(t)$ and is optimal for some important classes of functions.

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