The Math Forum

Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Math Forum » Discussions » sci.math.* » sci.math.symbolic

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: first anniversary of the IITS
Replies: 21   Last Post: Jan 10, 2015 4:01 PM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Albert D. Rich

Posts: 311
From: Hawaii Island
Registered: 5/30/09
Re: first anniversary of the IITS
Posted: Dec 21, 2014 2:30 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On Friday, December 19, 2014 9:13:37 AM UTC-10, wrote:

>> [...] A systematic check against the evaluations in Timofeev's book,
>> however, remains to be made.

> This referred to the trigonometric integration examples in Chapter 5
> of Timofeev's 1948 book, as provided in digitized form at
> <>. Such a check has now been made,
> with the result that seven integrands need to be corrected because they
> were typeset incorrectly or transcribed incorrectly or both.


I revised the 7 problems in the Timofeev test suite you flagged for correction pretty much as you suggested.

> While the next two integrals and their evaluations are correct, the
> evaluations can be improved in some respects.
> 1. Either of the following evaluations of Example 19.m (p. 220) is
> shorter than the version currently shown, the two differ in being
> discontinuous where SIN(x)^2 = 1 and where COS(x)^2 = 1, respectively:
> INT(SIN(x)^(2*m)*COS(x)^(2*m),x)=SIN(x)^(2*m+1)*COS(x)^(2*m+1)/(~
> 2*m+1)*F21(1,1+2*m,3/2+m,SIN(x)^2)=-SIN(x)^(2*m+1)*COS(x)^(2*m+1~
> )/(2*m+1)*F21(1,1+2*m,3/2+m,COS(x)^2)

Although shorter, and probably correct, I am unable to get Mathematica to verify these antiderivatives.

> 2. The evaluation of Example 45 (p. 254) can be continuitized in the
> customary manner:
> INT(1/(4-3*COS(x)^2+5*SIN(x)^2),x)=x/3+1/3*ATAN(2*SIN(x)*COS(x)/(2*SIN(x)^2+1))

I tweaked Rubi to give the continuous antiderivative you suggested.

> The remaining 29 items involve minor variations from the versions
> currently shown, such as a modified term order in the integrand and/or
> different trigonometric functions in the evaluation; they are offered
> here for inspection without much further comment.


The only suggestion I incorporated was to example 54 (p. 260). Although some of your suggestions resulted in slightly more compact results, they were not really simpler.

> I expect repercussions of the above on Rubi to be small.

Yes the repercussions were small, but resulted in a few nice improvements. The revised Timofeev test suite is now available at


Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2018. All Rights Reserved.