Rule: Q[4, 9, 30]

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.

• $P_1$:
  $16\cdot t^4-48\cdot t^2+12$
• $P_2$:
  $16\cdot t^{13}-528\cdot t^{11}+\frac{30276}{5}\cdot t^9-\frac{148968}{5}\cdot t^7+\frac{314307}{5}\cdot t^5-49329\cdot t^3+\frac{37611}{4}\cdot t$
• $P_3$:
  $16\cdot t^{43}-\frac{21153726462067795882451363812094283204298690842882552543352}{3742279853373169184537541659615992497050465474333728299}\cdot t^{41}+\frac{1872403239571727891168055877707354584099173726068577399637936}{2079044362985093991409745366453329165028036374629849055}\cdot t^{39}-\frac{56235967484099696859427056257990936569704930637313504130735568}{655041374639139202772933471622281791721162145431322305}\cdot t^{37}+\frac{2881567745338180246832140574342392198630693082820668758248031190441}{525998223835228779826665577712692278752093202781351810915}\cdot t^{35}-\frac{4745301864268152753535985620756219000174308978400980345188863342863}{19127208139462864720969657371370628318257934646594611306}\cdot t^{33}+\frac{867814850932755122636703561114806494696893167569357673218587429867174}{105199644767045755965333115542538455750418640556270362183}\cdot t^{31}-\frac{21624500236117479434462998269223053828693081564460816316208699129518361}{105199644767045755965333115542538455750418640556270362183}\cdot t^{29}+\frac{3268930837732690720862956202936853127675888330441970736227413245917981559}{841597158136366047722664924340307646003349124450162897464}\cdot t^{27}-\frac{94207068219106150639088952709015216736503215896547102416564101933836361587}{1683194316272732095445329848680615292006698248900325794928}\cdot t^{25}+\frac{11258117139784450250352218332585480237412580805990367303209608136139897925}{18295590394268827124405759224789296652246720096742671684}\cdot t^{23}-\frac{34206321336879254187241831456663881440482808974654473311762638206051757575}{6652941961552300772511185172650653328089716398815516976}\cdot t^{21}+\frac{1723071608458448191903159738107423162676962573217786610318321948564922254925}{53223535692418406180089481381205226624717731190524135808}\cdot t^{19}-\frac{16135747241478660071498797379770963116388503463365688356197365612770988145925}{106447071384836812360178962762410453249435462381048271616}\cdot t^{17}+\frac{27561325335113451029743005978321440258958879434726116621820925832367775615225}{53223535692418406180089481381205226624717731190524135808}\cdot t^{15}-\frac{133836100854494334094197971248086798827386482358963095643516127756503615035375}{106447071384836812360178962762410453249435462381048271616}\cdot t^{13}+\frac{3564862886922773342415208303641124748013721703242879435157549777923234207440375}{1703153142157388997762863404198567251990967398096772345856}\cdot t^{11}-\frac{7741443024254950983608160035652282151475358493691173252918640435699397210298875}{3406306284314777995525726808397134503981934796193544691712}\cdot t^9+\frac{34944510294120225712665012566877992253965284692535263121457581149561051514125}{23330864961060123257025526084911880164259827371188662272}\cdot t^7-\frac{457510649736481559837168781869793582404348255617418784862274255575311455212875}{851576571078694498881431702099283625995483699048386172928}\cdot t^5+\frac{2385615365261982802356954766028850916696658687318298919930367849522250547348125}{27250450274518223964205814467177076031855478369548357533696}\cdot t^3-\frac{239773608652933945420898189867943007336270399240784270269645330250346076768125}{54500900549036447928411628934354152063710956739096715067392}\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.