Rule: Q[4, 9, 44]

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.

• $P_1$:
  $t^4-6\cdot t^2+3$
• $P_2$:
  $t^{13}-66\cdot t^{11}+\frac{7569}{5}\cdot t^9-\frac{74484}{5}\cdot t^7+\frac{314307}{5}\cdot t^5-98658\cdot t^3+37611\cdot t$
• $P_3$:
  $t^{57}-\frac{11465785768001461668841949127181382159251254169531300091819916041099779978942864295346122143513045758}{8703986610742367046795711856486197746034458341636871004717655067288324834401606457896904361941759}\cdot t^{55}+\frac{664503474680331738985474268577722039056696428043323570674167960960389560990874687168342025526311700793114}{826878728020524869445592626366188785873273542455502745448177231392390859268152613500205914384467105}\cdot t^{53}-\frac{9236234009465228434885701705840497604179633007137181265387721817081171156421695215754991301995964996005167861}{30594512936759420169486927175548985077311121070853601581582557561518461792921646699507618832225282885}\cdot t^{51}+\frac{2396587467866809855927379982780924779596273648896812310266267744893397791308973617303127975998564505128645846963}{30594512936759420169486927175548985077311121070853601581582557561518461792921646699507618832225282885}\cdot t^{49}-\frac{13049420103063098418517228381886357248325434607279524297432819496559154742112326065523182594256546595049777996191}{874128941050269147699626490729971002208889173452960045188073073186241765512047048557360538063579511}\cdot t^{47}+\frac{9481205170680998138998669007651509667163918104791702677042458696569241778967646642889866718836216844213003828740304}{4370644705251345738498132453649855011044445867264800225940365365931208827560235242786802690317897555}\cdot t^{45}-\frac{215327327796068144004695889473042258093997240759811811296112316969163615643996160748428317143881195121300028149943349}{874128941050269147699626490729971002208889173452960045188073073186241765512047048557360538063579511}\cdot t^{43}+\frac{19430078153161049058649734482927513317877265410105340488625721118634383999144840688892812604944352120756449463061158785}{874128941050269147699626490729971002208889173452960045188073073186241765512047048557360538063579511}\cdot t^{41}-\frac{108415211395041554565800880728414372137662756196931239015439202026642139831416717713767545571803389143762299349016460847}{67240687773097626746125114671536230939145321034843080399082544091249366577849772965950810620275347}\cdot t^{39}+\frac{9063357634374875301428551777778936604539901688795330015885317198010020895001197780119305027968253754636962724622119990}{95648204513652385129623207214134041165213827930075505546347857882289283894523147888976971010349}\cdot t^{37}-\frac{433746158435662269585531127532564362227700103416312538550960860088944629233359843596421025544981861075930982769775024074}{95648204513652385129623207214134041165213827930075505546347857882289283894523147888976971010349}\cdot t^{35}+\frac{16950892764746564942338496669411656207568493884733857903155711300997343441296087083095878364266844976280025742045073147985}{95648204513652385129623207214134041165213827930075505546347857882289283894523147888976971010349}\cdot t^{33}-\frac{541423976574094544121480353871949676718665567197110700101488681697973388711964510672644353183879550633278269723915528990450}{95648204513652385129623207214134041165213827930075505546347857882289283894523147888976971010349}\cdot t^{31}+\frac{14121385189741525338946896910066036927409778748801900626371005674395640747196674187263900136513274866940113205616467879084640}{95648204513652385129623207214134041165213827930075505546347857882289283894523147888976971010349}\cdot t^{29}-\frac{299960124102127718677201602026553025731469299382641130993142480254455380043999351426581193377702907536286257019249577372614750}{95648204513652385129623207214134041165213827930075505546347857882289283894523147888976971010349}\cdot t^{27}+\frac{5166034599502545592385211493961718678630102252334961521715308900993637903752503572056781187515851285656660027281175018233130315}{95648204513652385129623207214134041165213827930075505546347857882289283894523147888976971010349}\cdot t^{25}-\frac{71670744727957395260934047336623532892829854211351724686818826825458505273063174514865555369326543933679595921679694207074791500}{95648204513652385129623207214134041165213827930075505546347857882289283894523147888976971010349}\cdot t^{23}+\frac{793912842896713224089637266403695385118897193531131956105241495594385665765524729072921416617277797443716977671815979381247848750}{95648204513652385129623207214134041165213827930075505546347857882289283894523147888976971010349}\cdot t^{21}-\frac{6939790281573387653530985080592865483004894245504447025721128772465119781235880193379272330748168374145164092980676532221859756625}{95648204513652385129623207214134041165213827930075505546347857882289283894523147888976971010349}\cdot t^{19}+\frac{47136032693272842534389396271426959974214367322539556009514930870286965265185729051778462565971240835442629575158560196612040343125}{95648204513652385129623207214134041165213827930075505546347857882289283894523147888976971010349}\cdot t^{17}-\frac{243757396698537849746608160537662691247923168248469707196609156098053298900975181183064177281461757483703592193604134549246060621625}{95648204513652385129623207214134041165213827930075505546347857882289283894523147888976971010349}\cdot t^{15}+\frac{934123259697447353447803126834542095537037060045318233686936904335945871288472206888816828077402898124450642416686845745113975810000}{95648204513652385129623207214134041165213827930075505546347857882289283894523147888976971010349}\cdot t^{13}-\frac{2557119476213109908727432927382559872513373510050743073030770506349572357057472493888095308792136685111720983486482680435085778046875}{95648204513652385129623207214134041165213827930075505546347857882289283894523147888976971010349}\cdot t^{11}+\frac{4750642588486757310832356819790763426301775410711889225287069419959435942904543384965069382418594523286365875462304422913665198418125}{95648204513652385129623207214134041165213827930075505546347857882289283894523147888976971010349}\cdot t^9-\frac{5558891367312060773565605291097989252431794915317177950272720737267447633698753479410721461041682623505685539336799740460053301965625}{95648204513652385129623207214134041165213827930075505546347857882289283894523147888976971010349}\cdot t^7+\frac{3646280957234823795462459719356308944949930484741522954648306773486410360736376445179084981519592669929645502842466677281916474646250}{95648204513652385129623207214134041165213827930075505546347857882289283894523147888976971010349}\cdot t^5-\frac{1092143306786688629185939100316329157931191810221471537087282397348657266473789731635786139129297781534810636098951481746132906975000}{95648204513652385129623207214134041165213827930075505546347857882289283894523147888976971010349}\cdot t^3+\frac{472146007741466733310347302935432719727344415726497176063664207996684453024420977117814006023633213169354163945719283889420165625}{480644243787197915224237222181578096307607175528017615810793255689895898967453004467220959851}\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 (probabilists') type can be downloaded here packed into a single file.