Rule: Q[6, 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.

• $P_1$:
  $64\cdot t^6-480\cdot t^4+720\cdot t^2-120$
• $P_2$:
  $64\cdot t^{50}-\frac{361666934392008231162093603961435390514828608}{10283796262563126106561632595159527911147}\cdot t^{48}+\frac{1185334114974870045756556672883219397130434004024}{133689351413320639385301223737073862844911}\cdot t^{46}-\frac{3460311038853437559096889970137899879569111129099180}{2540097676853092148320723251004403394053309}\cdot t^{44}+\frac{363044732953483589671469108018977095872669922584069830}{2540097676853092148320723251004403394053309}\cdot t^{42}-\frac{27620965516647967658771148153929696016983129359985783805}{2540097676853092148320723251004403394053309}\cdot t^{40}+\frac{243033971583649335721651675243508877354044070047360875215}{390784257977398792049342038616062060623586}\cdot t^{38}-\frac{1125320657397994934447253074161189753108226478183972502995}{41135185050252504426246530380638111644588}\cdot t^{36}+\frac{77275683253277674347754373243734564608959365136122836486225}{82270370100505008852493060761276223289176}\cdot t^{34}-\frac{4180573004581893996440079315963961989130139966859880756455825}{164540740201010017704986121522552446578352}\cdot t^{32}+\frac{89553727629345549566981456876066296772859972679497520159822575}{164540740201010017704986121522552446578352}\cdot t^{30}-\frac{3044371152392251160574408502621661566391562923499712243438093425}{329081480402020035409972243045104893156704}\cdot t^{28}+\frac{6311674854109002093840310078435222026191601739555872891331526325}{50627920061849236216918806622323829716416}\cdot t^{26}-\frac{134409007435010528837492151395489656906260411855779409313528111875}{101255840123698472433837613244647659432832}\cdot t^{24}+\frac{2248012864469671204005828133917522838220235231095132053870871945625}{202511680247396944867675226489295318865664}\cdot t^{22}-\frac{380524233050354946543944155782354295277567364989623923696327985801875}{5265303686432320566559555888721678290507264}\cdot t^{20}+\frac{952828636054181356808150429538724115390613544487110921851082418926875}{2632651843216160283279777944360839145253632}\cdot t^{18}-\frac{28897829495887660775820151991764808629334664045803356367822182967836875}{21061214745729282266238223554886713162029056}\cdot t^{16}+\frac{324734879624759312968613877930689988086689246857847835099916874504959375}{84244858982917129064952894219546852648116224}\cdot t^{14}-\frac{101056829246688293283558015039078676287157822026585893032890846113353125}{12960747535833404471531214495314900407402496}\cdot t^{12}+\frac{282840025339085177346743262196640573889117645943509535340666997587128125}{25921495071666808943062428990629800814804992}\cdot t^{10}-\frac{516906107792559986213377237959640538088629134834152397991756657023621875}{51842990143333617886124857981259601629609984}\cdot t^8+\frac{564524036859985806619198623084241954382865335848226076810412839474103125}{103685980286667235772249715962519203259219968}\cdot t^6-\frac{317497322877416021493557276788038777134390548449147437488603855263421875}{207371960573334471544499431925038406518439936}\cdot t^4+\frac{68529262256641426691379188887060772100110756054251100895191535012703125}{414743921146668943088998863850076813036879872}\cdot t^2-\frac{2351031588067984580369362913622700342502865269030033732515346147015625}{829487842293337886177997727700153626073759744}$

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.