Brahmagupta interpolation formula
- Brahmagupta interpolation formula
In trigonometry, the Brahmagupta interpolation formula is a special case of the Newton-Stirling interpolation formula to the second-order, which Brahmagupta used in 665 to interpolatenew values of the sine function from other values already tabulated. The formula gives an estimate for the value of a function at a value "a" + "xh" of its argument (with "h" > 0 and −1 ≤ "x" ≤ 1) when its value is already known at "a" − "h, a" and "a" + "h".
The formula for the estimate is:
:
where Δ is the first-order forward-difference operator, i.e.
:
References
*George G. Joseph (2000). "The Crest of the Peacock", p. 285–286. Princeton University Press. ISBN 0691006598.
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