 
					
					
						Woolhouse,s Formulas					
				 
				
					
						 المؤلف:  
						King, A. E
						 المؤلف:  
						King, A. E					
					
						 المصدر:  
						"Approximate Integration. Note on Quadrature Formulae: Their Construction and Application to Actuarial Functions." Trans. Faculty of Actuaries 9
						 المصدر:  
						"Approximate Integration. Note on Quadrature Formulae: Their Construction and Application to Actuarial Functions." Trans. Faculty of Actuaries 9					
					
						 الجزء والصفحة:  
						...
						 الجزء والصفحة:  
						...					
					
					
						 8-12-2021
						8-12-2021
					
					
						 943
						943					
				 
				
				
				
				
				
				
				
				
				
			 
			
			
				
				Woolhouse's Formulas
Let the values of a function  be tabulated at points
 be tabulated at points  equally spaced by
 equally spaced by  , so
, so  ,
,  , ...,
, ...,  . Then Woolhouse's formulas approximating the integral of
. Then Woolhouse's formulas approximating the integral of  are given by the Newton-Cotes-like formulas
 are given by the Newton-Cotes-like formulas
REFERENCES:
King, A. E. "Approximate Integration. Note on Quadrature Formulae: Their Construction and Application to Actuarial Functions." Trans. Faculty of Actuaries 9, 218-231, 1923.
Sheppard, W. F. "Some Quadrature-Formulæ." Proc. London Math. Soc. 32, 258-277, 1900.
Whittaker, E. T. and Robinson, G. "Woolhouse's Formulae." The Calculus of Observations: A Treatise on Numerical Mathematics, 4th ed. New York: Dover, p. 158, 1967.
Woolhouse, W. S. B. "On Integration by Means of Selected Values of the Function." J. Inst. Act. 27, 122-155, 1888.
 
				
				
					
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