5
$\begingroup$

Looking into this question made me suspect that SumConvergence might have more Methods available than the four listed in its documentation. How do I find all Methods available for this function?

Edit: For completeness let me add that, besides Automatic, the documentation mentions (note the vague choice of words: "possible values ... include")

Possible values for Method include:
"IntegralTest" the integral test
"RaabeTest" Raabe's test
"RatioTest" D'Alembert ratio test
"RootTest" Cauchy root test

Note: The obvious adaption to the answer to this similar question does not seem to work; the same seems to be true for the answers to this question.

Improve this question
$\endgroup$
6
  • 1
    $\begingroup$ The code within Sum`SumConvergenceDump`SumConvergenceTestMethod[] seems to show the names of the supported methods. $\endgroup$
    – J. M.'s missing motivation ♦
    Commented Dec 12, 2016 at 13:17
  • $\begingroup$ @J.M: Probably I'm very naive, but if I evaluate that noting happens; I just get back the input. $\endgroup$
    – Jules Lamers
    Commented Dec 12, 2016 at 13:22
  • 3
    $\begingroup$ You need to have run SumConvergence[] first before trying ??Sum`SumConvergenceDump`SumConvergenceTestMethod. $\endgroup$
    – J. M.'s missing motivation ♦
    Commented Dec 12, 2016 at 13:22
  • 1
    $\begingroup$ I also see "DivergenceTest" in the code. $\endgroup$
    – J. M.'s missing motivation ♦
    Commented Dec 12, 2016 at 13:31
  • 1
    $\begingroup$ Can't really say; that's what I got after cursory spelunking. Someone else who knows more than me might want to chime in instead. $\endgroup$
    – J. M.'s missing motivation ♦
    Commented Dec 12, 2016 at 13:39

1 Answer 1

Reset to default
3
$\begingroup$

Like J.M., I see the "DivergenceTest" (Nth term test for divergence) as well as user-defined methods.

The "DivergenceTest" can only be used to show divergence (return value False). If it returns True, it is unreliable.

SumConvergence[1/n, n, Method -> "DivergenceTest"]
(*  True  *)

User-defined methods have the form Method -> myConvTest, where myConvTest has the form as SumConvergence (without options):

myConvTest[summand, variable]

Examples:

SumConvergence[1/n, n, Method -> (True &)] (* the optimistic test *)
(*  True  *)

myLCT[e_, k_] := SumConvergence[Normal[Series[e, {k, ∞, 2}]], k]
SumConvergence[Sin[50/n^2], n, Method -> myLCT]
(*  True  *)

[Discovered exploring this question.]

Improve this answer
$\endgroup$
1
  • $\begingroup$ Thanks, that is a useful addition to J.M.'s comments! $\endgroup$
    – Jules Lamers
    Commented Jan 13, 2018 at 15:21

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.