Bessel,s Finite Difference Formula
المؤلف:
Abramowitz, M. and Stegun, I. A.
المصدر:
Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover
الجزء والصفحة:
...
25-11-2021
1650
Bessel's Finite Difference Formula
An interpolation formula, sometimes known as the Newton-Bessel formula, given by
 |
(1)
|
for ![p in [0,1]](https://mathworld.wolfram.com/images/equations/BesselsFiniteDifferenceFormula/Inline1.gif)
, where 
is the central difference and
where 
are the coefficients from Gauss's backward formula and Gauss's forward formula and 
and 
are the coefficients from Everett's formula. The 
s also satisfy
for
 |
(12)
|
REFERENCES:
Abramowitz, M. and Stegun, I. A. (Eds.). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, p. 880, 1972.
Acton, F. S. Numerical Methods That Work, 2nd printing. Washington, DC: Math. Assoc. Amer., pp. 90-91, 1990.
Beyer, W. H. CRC Standard Mathematical Tables, 28th ed. Boca Raton, FL: CRC Press, p. 433, 1987.
Whittaker, E. T. and Robinson, G. "The Newton-Bessel Formula." §24 in The Calculus of Observations: A Treatise on Numerical Mathematics, 4th ed. New York: Dover, pp. 39-40, 1967.
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