NSum

Usage

• NSum[f, {i, , }] gives a numerical approximation to the sum .
• NSum[f, {i, , , di}] uses a step di in the sum.

Notes

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

• NSum[f, {i, ... }, {j, ... }, ... ] can be used to evaluate multidimensional sums.

• The following options can be given:

AccuracyGoal	Infinity	number of digits of final accuracy to try and get
EvaluationMonitor	None	expression to evaluate whenever f is evaluated
Method	Automatic	method to use: Integrate or Fit
NSumExtraTerms	12	maximum number of terms to use in extrapolation
NSumTerms	15	number of terms to use before extrapolation
PrecisionGoal	Automatic	number of digits of final precision to try and get
VerifyConvergence	True	whether to explicitly test for convergence
WorkingPrecision	MachinePrecision	the precision used in internal computations

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

• 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.

• 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.

• VerifyConvergence is only used for sums with infinite limits.

• N[Sum[ ... ]] calls NSum.

• NSum has attribute HoldAll.

• See Section 1.6.2, Section 3.9.1 and Section 3.9.4.

• Implementation notes: see Section A.9.4.

• See also: NProduct.

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

• New in Version 1; modified in 5.

Further Examples