Rule: Q[2, 3, 6, 34]

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.

• $P_1$:
  $4\cdot t^2-2$
• $P_2$:
  $4\cdot t^5-14\cdot t^3+6\cdot t$
• $P_3$:
  $4\cdot t^{11}-\frac{6923}{82}\cdot t^9+\frac{97479}{164}\cdot t^7-\frac{566685}{328}\cdot t^5+\frac{1313235}{656}\cdot t^3-\frac{418635}{656}\cdot t$
• $P_4$:
  $4\cdot t^{45}-\frac{63617803672860193255376503302073329669785621715477162873837730021251674057501736424499613467087}{37227337747657733999220732121545047939623620469646081915161264890790592203505597602052830190}\cdot t^{43}+\frac{12850315980269882203459774043746715654092756467535425355950388740045118123011033254404620445619914013}{38865340608554674295186444334893030048967059770310509519428360545985378260459843896543154718360}\cdot t^{41}-\frac{20918118055079616890714391149900087304589641574203412583392726603048617989135563560025405559971680066443}{544114768519765440132610220688502420685538836784347133271997047643795295646437814551604166057040}\cdot t^{39}+\frac{31158178403527736267090416059375313560017996705231088183096899083549316340023235566227866709900867589585}{10364090828947913145383051822638141346391215938749469205180896145596100869455958372411507924896}\cdot t^{37}-\frac{593447225693716427926612519884031145403392080145336957873851275754490024710597624165562052370530430941535}{3538957844030994732569822573583755581694561540060794362744696244837692979814229688140514901184}\cdot t^{35}+\frac{143138390930528475950805883257877561526047289920444809522075167984509902335546014392734058361144573854732619}{20728181657895826290766103645276282692782431877498938410361792291192201738911916744823015849792}\cdot t^{33}-\frac{1481525617062542995521121761385763836904044832105593201542167404415509649867850156058684356761646902982007577}{6909393885965275430255367881758760897594143959166312803453930763730733912970638914941005283264}\cdot t^{31}+\frac{2422835599756431192364902880454615918627008730993936425057924050879424950838281542538887695116643466555133719}{476509923170018995190025371155776613627182342011469848514064190602119580204871649306276226432}\cdot t^{29}-\frac{11044097174739700000325773844495851280728189719018203941117662550299005205974356016047212458375741810992923805}{119127480792504748797506342788944153406795585502867462128516047650529895051217912326569056608}\cdot t^{27}+\frac{4966329964224664756473594756105055532659592004453586625784685536322993022501780459392866102293093085060012003735}{3812079385360151961520202969246212909017458736091758788112513524816956641638973194450209811456}\cdot t^{25}-\frac{107407459036546260697641824200417939381170988036200058570464268579851783403351679220171843419174496943329039214875}{7624158770720303923040405938492425818034917472183517576225027049633913283277946388900419622912}\cdot t^{23}+\frac{1778216481844191100381554898366552777714812403321056155759594962457420892420218027599368550220058676073272727676225}{15248317541440607846080811876984851636069834944367035152450054099267826566555892777800839245824}\cdot t^{21}-\frac{22334345639859285789809488167954706500393490316605836077842821980533966475905256297113281911519389014999795330797925}{30496635082881215692161623753969703272139669888734070304900108198535653133111785555601678491648}\cdot t^{19}+\frac{52499124617310415565883399881349606947708246737207710457298645874830083522122165760095059281203253753539333115938375}{15248317541440607846080811876984851636069834944367035152450054099267826566555892777800839245824}\cdot t^{17}-\frac{725428369976963889982367460066222737948432574743402512025203351927054473757609505343183393842371361472267310808171625}{60993270165762431384323247507939406544279339777468140609800216397071306266223571111203356983296}\cdot t^{15}+\frac{3590573739930134994344709321249286093040106395679907442304184992456584485267821118683163955207451657297984370779457125}{121986540331524862768646495015878813088558679554936281219600432794142612532447142222406713966592}\cdot t^{13}-\frac{24603768212199835581711530175594565480133407295954428884527433434860703962018969486689648248531006765283711309882107625}{487946161326099451074585980063515252354234718219745124878401731176570450129788568889626855866368}\cdot t^{11}+\frac{111400171208732382939671916299837785256070340205474241615134144365908118109478864381299699284656275937348130839760585125}{1951784645304397804298343920254061009416938872878980499513606924706281800519154275558507423465472}\cdot t^9-\frac{156415579995387602111693119206686034121903463440478880705991086174996357467102306628901844739584199739282191638656138125}{3903569290608795608596687840508122018833877745757960999027213849412563601038308551117014846930944}\cdot t^7+\frac{124541462855582016673833688806124615238318926130525509516652385904785496112149541185247781997724301150093187337359929375}{7807138581217591217193375681016244037667755491515921998054427698825127202076617102234029693861888}\cdot t^5-\frac{48432679361416675926607217107951037416435900745033859062591985543622179010955770232012193504205150369082181736532094375}{15614277162435182434386751362032488075335510983031843996108855397650254404153234204468059387723776}\cdot t^3+\frac{3137452362316710645890774916760504885959036996753432480758448518634371955238148441229356333708889716192180089302346875}{15614277162435182434386751362032488075335510983031843996108855397650254404153234204468059387723776}\cdot t$

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.