numlib::Lambda -- von Mangoldt's
function
Introductionnumlib::Lambda(m) returns the value of von
Mangoldt's function at m.
Call(s)numlib::Lambda(m)
Parametersm |
- | arithmetical expression |
Returnsnumlib::Lambda returns an arithmetical expression
Related
Functions
Detailsm is a number but not a natural
number.m is not a number, numlib::Lambda
returns the unevaluated function call.
Example
1numlib::Lambda takes on nonzero values only
for prime powers:
>> numlib::Lambda(49)
ln(7)
>> numlib::Lambda(48)
0
Example
2numlib::Lambda returns the function call if
its argument is not a number:
>> numlib::Lambda(3+n^4)
4
numlib::Lambda(n + 3)
BackgroundLambda at m is
defined to be log p if m=p^n for some prime
number p and some positive integer n, and to be
zero for positive integers that are not prime powers.