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Documentation / Mathematica / Built-in Functions / Numerical Computation / Sums and Products /

NSum

FilledSmallSquare NSum[f, i, imin, imax] gives a numerical approximation to the sum .

FilledSmallSquare NSum[f, i, imin, imax, di] uses a step di in the sum.

FilledSmallSquare NSum can be used for sums with both finite and infinite limits.

FilledSmallSquare NSum[f, i, ... , j, ... , ... ] can be used to evaluate multidimensional sums.

FilledSmallSquare The following options can be given:

FilledSmallSquare NSum uses either the Euler-Maclaurin (Integrate) or Wynn epsilon (Fit) method.

FilledSmallSquare With the Euler-Maclaurin method, the options AccuracyGoal and PrecisionGoal can be used to specify the accuracy and precision to try and get in the final answer. NSum stops when the error estimates it gets imply that either the accuracy or precision sought has been reached.

FilledSmallSquare You should realize that with sufficiently pathological summands, the algorithms used by NSum can give wrong answers. In most cases, you can test the answer by looking at its sensitivity to changes in the setting of options for NSum.

FilledSmallSquare VerifyConvergence is only used for sums with infinite limits.

FilledSmallSquare N[Sum[ ... ]] calls NSum.

FilledSmallSquare NSum has attribute HoldAll.

FilledSmallSquare See Section 1.6.2, Section 3.9.1 and Section 3.9.4.

FilledSmallSquare Implementation Notes: see Section A.9.4.

FilledSmallSquare See also: NProduct.

FilledSmallSquare Related packages: NumericalMath`ListIntegrate`, NumericalMath`NLimit`.

FilledSmallSquare New in Version 1; modified in 5.0.

Further Examples