Rule: Q[1, 8, 56]

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.

• $P_1$:
  $2\cdot t$
• $P_2$:
  $2\cdot t^9-36\cdot t^7+189\cdot t^5-315\cdot t^3+\frac{945}{8}\cdot t$
• $P_3$:
  $2\cdot t^{65}-\frac{48756443636972876374566540204142356882643669712300959510316795886366760}{26329924825818023815358945523436194015742759935352760191605320169273}\cdot t^{63}+\frac{176073695858275382267364466816182275680128253425460542693435414035216864868}{219416040215150198461324546028634950131189666127939668263377668077275}\cdot t^{61}-\frac{47513966295112218405083583062749136515161461355531672372041400138793124639646}{219416040215150198461324546028634950131189666127939668263377668077275}\cdot t^{59}+\frac{35845507046591040784580030080798344022447089524954257877628147599453602327184913}{877664160860600793845298184114539800524758664511758673053510672309100}\cdot t^{57}-\frac{1256916644071043844459322147733356786890152518526961416812731846110976132629962089}{219416040215150198461324546028634950131189666127939668263377668077275}\cdot t^{55}+\frac{43585615756238156441995675591362526048472604848253235956118268872991788793074265229}{70213132868848063507623854729163184041980693160940693844280853784728}\cdot t^{53}-\frac{275198189067762920449639714410169296729119732906582622354097345855654958320381557363}{5162730358003534081442930494791410591322109791245639253255945131230}\cdot t^{51}+\frac{121969034495127784746588728257128928046607013925660036835129038662851006245552369894889}{33041474291222618121234755166665027784461502663972091220838048839872}\cdot t^{49}-\frac{3448554105942877674156149005684403614736421980711776323459288762219915520865325518646069}{16520737145611309060617377583332513892230751331986045610419024419936}\cdot t^{47}+\frac{80328587847208559373725534963499473620685138361802171733151378734881071743967641019046209}{8260368572805654530308688791666256946115375665993022805209512209968}\cdot t^{45}-\frac{24817771679280220000849159193618849171593810803327788708664066059765398968337834487190581625}{66082948582445236242469510333330055568923005327944182441676097679744}\cdot t^{43}+\frac{6382396315847745584151884325723171418962675191886867404014182148427193164252773377483560628825}{528663588659561889939756082666640444551384042623553459533408781437952}\cdot t^{41}-\frac{21399322549084050527964715240635387111980709366561477128647004751145524625122934058096526186765}{66082948582445236242469510333330055568923005327944182441676097679744}\cdot t^{39}+\frac{7670285663258705585398912117594872902174811109456719969182099581430182574486165854499129943501855}{1057327177319123779879512165333280889102768085247106919066817562875904}\cdot t^{37}-\frac{71729147426426518860958324663988106587353133749669303092531823474918620859758161885238054890864805}{528663588659561889939756082666640444551384042623553459533408781437952}\cdot t^{35}+\frac{2236454758776111005133269959898741595400139577406376570926910264474949791271529284965515666116543375}{1057327177319123779879512165333280889102768085247106919066817562875904}\cdot t^{33}-\frac{694102673422455608542970160365987300343444781711205330084879253993782766491239583204125848258811575}{25325201851955060595916459049898943451563307431068429199205211086848}\cdot t^{31}+\frac{2486516725431785113411237868375076114161129858060405402577127740496824515161421350534554103490891523525}{8458617418552990239036097322666247112822144681976855352534540503007232}\cdot t^{29}-\frac{43910264608902810843465955512896137518174979121820475690866048147345727888652917977536699788384334325225}{16917234837105980478072194645332494225644289363953710705069081006014464}\cdot t^{27}+\frac{15183195171249769798341311792876621002299758102299987445932256946235136848298128680135651656995860089925}{810406459262561939069326689596766190450025837794189734374566754779136}\cdot t^{25}-\frac{3707648392907208704371098616944039864915210950784050228698819545343938812248261212873060859314945101690625}{33834469674211960956144389290664988451288578727907421410138162012028928}\cdot t^{23}+\frac{139045326437661190283017354440714961641046897686819042751264510533240278370317894902067495722719138744466875}{270675757393695687649155114325319907610308629823259371281105296096231424}\cdot t^{21}-\frac{64413879143523058522557824730701790932431670313090055720359098368403019403331755693559561515850117195218125}{33834469674211960956144389290664988451288578727907421410138162012028928}\cdot t^{19}+\frac{11872960188970214470488119500503339813092488348054255055502910026734769349531445330903947808992976368049229375}{2165406059149565501193240914602559260882469038586074970248842368769851392}\cdot t^{17}-\frac{13000233832134552115763916206398404106223572083503524327394913632317457618558584198800483659721415670494291875}{1082703029574782750596620457301279630441234519293037485124421184384925696}\cdot t^{15}+\frac{21047251402042403062595053380443104805699544298144399797210627292310369871431081170201062388855428981050296875}{1082703029574782750596620457301279630441234519293037485124421184384925696}\cdot t^{13}-\frac{97106493597757717297999007144767861832053368301455313886304415800660531770160435650573566380252063443362194375}{4330812118299131002386481829205118521764938077172149940497684737539702784}\cdot t^{11}+\frac{607083255393716640074179231373552519203031289255620974681780251118995723899294460398008299695034225792357106875}{34646496946393048019091854633640948174119504617377199523981477900317622272}\cdot t^9-\frac{18703170972795345256786027890357288945886951677771238756262060139223453709515623713878993571630723428032073125}{2165406059149565501193240914602559260882469038586074970248842368769851392}\cdot t^7+\frac{166793765802262727840634957397092415195132095196089546752599201968219302846323268899923817588111497235611095625}{69292993892786096038183709267281896348239009234754399047962955800635244544}\cdot t^5-\frac{10848165662890142607042534440263925107422133563844438039421072258237071234011103893993661066169143012928015625}{34646496946393048019091854633640948174119504617377199523981477900317622272}\cdot t^3+\frac{13556758378337454458626117896759264645633286272527541101598186980644171057071585514880117385709841584287628125}{1108687902284577536610939348276510341571824147756070384767407292810163912704}\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.