Rule: Q[6, 49]

Type

Polynomials

One starts from the polynomial $P_1$ and extends one by one with $P_{\mathrm{i}}$ until the final polynomial defining this rule is reached.
Note: Polynomials might be truncated due to size! The complete polynomials are included in the download.

• $P_1$:
  $64\cdot t^6-480\cdot t^4+720\cdot t^2-120$
• $P_2$:
  $64\cdot t^{55}-\frac{14440367788501149589734194937778315146842228731816561760}{338071256417604147929271014526164762694207273539701}\cdot t^{53}+\frac{49010137556373613971617318317329952785115808207948674302320}{3718783820593645627221981159787812389636280008936711}\cdot t^{51}-\frac{4489339539088243368635745469205303131366943592683411586915960}{1796715778489064741242080785066021716341124049261557}\cdot t^{49}+\frac{52188561680066777480079720643404323048737967013322562277084741720}{159907704285526761970545189870875932754360040384278573}\cdot t^{47}-\frac{4991108735880619165398809831033658880993778703058612902546935004180}{159907704285526761970545189870875932754360040384278573}\cdot t^{45}+\frac{32963953366630701802956231783154683537333703592299744209889832523450}{14537064025956978360958653624625084795850912762207143}\cdot t^{43}-\frac{43327217571970470371063012595836369869808293222210092169463906076525}{338071256417604147929271014526164762694207273539701}\cdot t^{41}+\frac{7741900548580754677214243575121618458662201522649186822619102678077575}{1352285025670416591717084058104659050776829094158804}\cdot t^{39}-\frac{29076851698398510152833391154955370022790354418138404272706202684097675}{142345792175833325443903585063648321134403062543032}\cdot t^{37}+\frac{1668301435827925743750985974349213840302843609548357078255098256128977525}{284691584351666650887807170127296642268806125086064}\cdot t^{35}-\frac{4065295151665844901210824515166617824952311426482425323639299643775507125}{29967535194912279040821807381820699186190118430112}\cdot t^{33}+\frac{722248293396061028619346267453105926485336905697204572030184048295381514875}{284691584351666650887807170127296642268806125086064}\cdot t^{31}-\frac{1147330209765929369420702284546343369018800130495870235103205311764128142375}{29967535194912279040821807381820699186190118430112}\cdot t^{29}+\frac{529261256851069002126001523600176587952080666039804269083761247444911451926375}{1138766337406666603551228680509186569075224500344256}\cdot t^{27}-\frac{10281986957869737462568131612676930958787997425769292993051063644788392348134125}{2277532674813333207102457361018373138150449000688512}\cdot t^{25}+\frac{634536288777780564814503894722473883214695391693166437980564062530948389632790625}{18220261398506665656819658888146985105203592005508096}\cdot t^{23}-\frac{7697018965317305490353286562133365191485313981658527762487679304473272882316784375}{36440522797013331313639317776293970210407184011016192}\cdot t^{21}+\frac{72452797542102041637142978290235383589697801659554133765696861074679083335175590625}{72881045594026662627278635552587940420814368022032384}\cdot t^{19}-\frac{27387898630214713066417356856280458413206309047161201551541975176619656685081440625}{7671689009897543434450382689746098991664670318108672}\cdot t^{17}+\frac{1394751157514311111147828215641595778825345622834899881378171874888344468916157315625}{145762091188053325254557271105175880841628736044064768}\cdot t^{15}-\frac{5419208847605167481890612925576385061806854681686246829241061024696801628827315734375}{291524182376106650509114542210351761683257472088129536}\cdot t^{13}+\frac{14657574470927109697616566355061292096466151762910977431666209218203563295640734203125}{583048364752213301018229084420703523366514944176259072}\cdot t^{11}-\frac{26030206564680774376167838895587504485720954956007282713283636290203494425050482984375}{1166096729504426602036458168841407046733029888352518144}\cdot t^9+\frac{55419124056555958030372154729067193657452057866516426039550719731162827761120222296875}{4664386918017706408145832675365628186932119553410072576}\cdot t^7-\frac{30160231788089941534287376467415081947935734052196563660506576851267099079186735078125}{9328773836035412816291665350731256373864239106820145152}\cdot t^5+\frac{5917386825307713939043380126258033542434490762153289339140924397290006621137486171875}{18657547672070825632583330701462512747728478213640290304}\cdot t^3-\frac{50921732550984757027110272708475065757538784426139582027427669641357679954964765625}{37315095344141651265166661402925025495456956427280580608}\cdot t$

Warning: This rule has negative weights!

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

All rules of Hermite (physicists') type can be downloaded here packed into a single file.