DLMF

For nearly 50 years, a stan­dard ref­er­ence in math­e­mat­i­cal work has been Abramowitz and Stegun’s (1964) Hand­book of Math­e­mat­i­cal Func­tions with For­mu­las, Graphs, and Math­e­mat­i­cal Tables. It has pro­vided a mar­vel­lous col­lec­tion of results and tables that have been indis­pens­able for a gen­er­a­tion of math­e­mati­cians. I’ve used it to look up com­pu­ta­tion­ally effi­cient meth­ods for cal­cu­lat­ing Bessel func­tions or gamma func­tions, or to find one of those trigono­met­ric iden­ti­ties I learned in high school and no longer remem­ber. Appar­ently nearly 1 mil­lion copies of the hand­book have been printed and it has also been scanned and put online.

Lately, the hand­book has fallen out of favour a lit­tle, partly because there is not such a need for it. We no longer need tables for trigono­met­ric func­tions or log­a­rithms, and a lot of func­tions are built into R, includ­ing Bessel func­tions and vari­a­tions on the gamma func­tion. Another rea­son for its declin­ing pop­u­lar­ity has been the rise of online resources: if you want to know some­thing about orthog­o­nal poly­no­mi­als, there is a good chance it is cov­ered in the Wikipedia arti­cle.

Now the hand­book has been reis­sued as the NIST Hand­book of Math­e­mat­i­cal Func­tions (Cam­bridge Uni­ver­sity Press) with a free web edi­tion called the NIST Dig­i­tal Library of Math­e­mat­i­cal Func­tions (DLMF). It has been updated to include colour graph­ics, point­ers to rec­om­mended soft­ware, and lots of new top­ics to reflect work from the last 50 years.

Wol­fra­mAl­pha

Wol­fra­mAl­pha is now a year old and it has become a remark­able resource for some things. It was orig­i­nally com­pared to Google which is inap­pro­pri­ate — they are intended for dif­fer­ent pur­poses. Google indexes the web, while Wol­fra­mAl­pha is a knowl­edge engine.

Recently I needed to find the inte­gral of . Typ­ing integral 2tan(2x)sec^6(2x) gave me the result straight away. Of course, I could use Math­e­mat­ica or Maple for this, but it is much eas­ier to use my browser. It also means such alge­braic results are avail­able to every­one with­out need­ing spe­cial­ist sym­bolic alge­bra software.

A few days later, I was work­ing on a project involv­ing mod­el­ling elec­tric­ity demand as a func­tion of tem­per­a­ture. The tem­per­a­ture data looked odd and I sus­pected it was all out by one day. To check, I typed melbourne temperature 21 February 2010 into Wol­fra­mAl­pha and it promptly gave me the tem­per­a­ture data for Mel­bourne Air­port for that day, and with one more click of the mouse I had the data for the whole week, con­firm­ing my suspicion.

For the sorts of things that Wol­fra­mAl­pha is good at, see the exam­ples page.

Wikipedia

Wikipedia needs no intro­duc­tion and it is sur­pris­ingly good in some areas of math­e­mat­ics (e.g., prob­a­bil­ity dis­tri­b­u­tions) but not very good for some areas of sta­tis­tics (e.g., see the arti­cle on ARIMA mod­els or the one on Cronbach’s alpha). The good news is that the sta­tis­tics arti­cles are improv­ing and is now start­ing to be usable as a first port of call when look­ing up an unfa­mil­iar method.

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