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numlib::Lambda

Von Mangoldt's function

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Syntax

numlib::Lambda(m)

Description

numlib::Lambda(m) returns the value of von Mangoldt's function at m.

It is an error if m is a number but not a natural number.

If m is not a number, numlib::Lambda returns the unevaluated function call.

Examples

Example 1

numlib::Lambda takes on non-zero values only for prime powers:

numlib::Lambda(49)

numlib::Lambda(48)

Example 2

numlib::Lambda returns the function call if its argument is not a number:

numlib::Lambda(3+n^4)

Parameters

m

Arithmetical expression

Return Values

numlib::Lambda returns an arithmetical expression

Algorithms

The function value of Lambda at m is defined to be logp if m = pn for some prime number p and some positive integer n, and to be zero for positive integers that are not prime powers.

See Also

MuPAD Functions

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