Spencer,s Formula
المؤلف:
Whittaker, E. T. and Robinson, G.
المصدر:
"Spencer,s Formula." §144 in The Calculus of Observations: A Treatise on Numerical Mathematics, 4th ed. New York: Dover
الجزء والصفحة:
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4-5-2021
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Spencer's Formula
Define the notation
![[n]f_0=f_(-(n-1)/2)+...+f_0+...+f_((n-1)/2)](https://mathworld.wolfram.com/images/equations/SpencersFormula/NumberedEquation1.gif) |
(1)
|
and let 
be the central difference, so
 |
(2)
|
Spencer's 21-term moving average formula is then given by
 |
(3)
|
which, written explicitly, gives
 |
(4)
|
REFERENCES:
Spencer, J. J. I. A. 38, 334, 1904.
Spencer, J. J. I. A. 38, 339, 1904.
Spencer, J. J. I. A. 41, 361, 1907.
Whittaker, E. T. and Robinson, G. "Spencer's Formula." §144 in The Calculus of Observations: A Treatise on Numerical Mathematics, 4th ed. New York: Dover, pp. 290-294, 1967.
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