Rule: Q[1, 8, 46]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^9-36\cdot t^7+378\cdot t^5-1260\cdot t^3+945\cdot t$
• $P_3$:
  $t^{55}-\frac{548021610530340394586625212026451608382200156825}{424222306338984413743764211130890177598635909}\cdot t^{53}+\frac{1634667362191901076226208303565501284463694854954561}{2121111531694922068718821055654450887993179545}\cdot t^{51}-\frac{23343202826978716167524696596804970012244555880242006991}{82723349736101960680034021170523584631734002255}\cdot t^{49}+\frac{111746242095965869450252877522007330735267481245692019635086}{1571743644985937252920646402239948108002946042845}\cdot t^{47}-\frac{20587369819889827796533464687756413113935268617859379647415254}{1571743644985937252920646402239948108002946042845}\cdot t^{45}+\frac{191813733490534186642204120136362285363479574747601487915842250}{104782909665729150194709760149329873866863069523}\cdot t^{43}-\frac{507883613442152359587036629449274819492686198152323706060107034}{2555680723554369516944140491447070094313733403}\cdot t^{41}+\frac{3346715155815395560490739243344203894866575242948316295148156869}{196590824888797655149549268572851545716441031}\cdot t^{39}-\frac{12030853034564456381535729173056919108493857198170199319698588979}{10346885520463034481555224661729028721917949}\cdot t^{37}+\frac{659441636556025226755935615625313666381847770135903727834786641511}{10346885520463034481555224661729028721917949}\cdot t^{35}-\frac{29107649598758034685756517797538230078531021613251452837880072382175}{10346885520463034481555224661729028721917949}\cdot t^{33}+\frac{1035618967980280278395972851960416640762562689960867826127073276432020}{10346885520463034481555224661729028721917949}\cdot t^{31}-\frac{29661965413242695667729001501230968299130373195759820997488608750208260}{10346885520463034481555224661729028721917949}\cdot t^{29}+\frac{681618372041337998613326513573599445218705003007484952354841119442008740}{10346885520463034481555224661729028721917949}\cdot t^{27}-\frac{12498220905097287090715181798602022437152333703922411352979736294552231460}{10346885520463034481555224661729028721917949}\cdot t^{25}+\frac{181461108307881126235189760849055514855632429569960814997524040745695186875}{10346885520463034481555224661729028721917949}\cdot t^{23}-\frac{2065107696196375368397229868808347021013926686681436381447136670688389682375}{10346885520463034481555224661729028721917949}\cdot t^{21}+\frac{18183543082252591704870030244486982951372684505010968593658831177039564775875}{10346885520463034481555224661729028721917949}\cdot t^{19}-\frac{121851965967107644363757590669590336845829576487440911003781649629747181072875}{10346885520463034481555224661729028721917949}\cdot t^{17}+\frac{608593030566790415204254876120286557599946329694957289462775160945357782642750}{10346885520463034481555224661729028721917949}\cdot t^{15}-\frac{2205655474338515824316162459157942422798176447765965083866704264292000663743750}{10346885520463034481555224661729028721917949}\cdot t^{13}+\frac{5601491403456894169921084847786884975346379709574077110636620373630339963963750}{10346885520463034481555224661729028721917949}\cdot t^{11}-\frac{9512319692397405388012919736861660288367160233496137406752864248000537137703750}{10346885520463034481555224661729028721917949}\cdot t^9+\frac{10116011610869745103850621991344275184756764863832288584166625597568306853430625}{10346885520463034481555224661729028721917949}\cdot t^7-\frac{6103426311970099575963446885908647339031125602766122565194216918218156309963125}{10346885520463034481555224661729028721917949}\cdot t^5+\frac{1758588766897228875833203668080943799103125286648268616785672533262182602640625}{10346885520463034481555224661729028721917949}\cdot t^3-\frac{160333823114756615977209943896885593936798847647557626187042036534221960665625}{10346885520463034481555224661729028721917949}\cdot t$

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.