Rule: Q[3, 68]

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.

• $P_1$:
  $8\cdot t^3-12\cdot t$
• $P_2$:
  $8\cdot t^{71}-\frac{2729272810348417914549476406155913343948}{281883215233401101190419706483682719}\cdot t^{69}+\frac{519370473179620046678538371788416000132538}{93961071744467033730139902161227573}\cdot t^{67}-\frac{16923131749860167100598912556807256541028607}{8541915613133366702739991105566143}\cdot t^{65}+\frac{4276311688532796285741365311262670040180469660}{8541915613133366702739991105566143}\cdot t^{63}-\frac{811004561546510664176365708769640045054140842950}{8541915613133366702739991105566143}\cdot t^{61}+\frac{119993931174191347596485022768076296267307984098555}{8541915613133366702739991105566143}\cdot t^{59}-\frac{28429405677879375735470440633909547567266226683774155}{17083831226266733405479982211132286}\cdot t^{57}+\frac{10984017605322382279863016810357642012616703128472002205}{68335324905066933621919928844529144}\cdot t^{55}-\frac{1753075886953197450810099088284586800072539998669489233225}{136670649810133867243839857689058288}\cdot t^{53}+\frac{233404106152086211546017895514130415659126044601243318541725}{273341299620267734487679715378116576}\cdot t^{51}-\frac{26106709339052528483842297658624734735638772606084959222721125}{546682599240535468975359430756233152}\cdot t^{49}+\frac{1232828285058821785385866259432015120610427021172446337836282125}{546682599240535468975359430756233152}\cdot t^{47}-\frac{98656035793607639903353860631717162811361005661778059794902052625}{1093365198481070937950718861512466304}\cdot t^{45}+\frac{6703548675496484420935319563070612685925051604096851169405319050625}{2186730396962141875901437723024932608}\cdot t^{43}-\frac{387128516156389001212035090684481805297412412031071680249502375670625}{4373460793924283751802875446049865216}\cdot t^{41}+\frac{75994197419817376258171608452783109014938027086580148620664931621193125}{34987686351394270014423003568398921728}\cdot t^{39}-\frac{3165684901731357669735066663329315230966748452513637451030868840374230625}{69975372702788540028846007136797843456}\cdot t^{37}+\frac{111699923277583231979789580795195532981977274389963998744944857113678248125}{139950745405577080057692014273595686912}\cdot t^{35}-\frac{3327913452037274050354321502794095233622104702208917369581042233917812003125}{279901490811154160115384028547191373824}\cdot t^{33}+\frac{20841847108414683149696323637790854030115742251821465958922470441114356315625}{139950745405577080057692014273595686912}\cdot t^{31}-\frac{436645306024917203270484204336686475048638141100704568312079947349646968378125}{279901490811154160115384028547191373824}\cdot t^{29}+\frac{7599444681253853069993782928074983636761529442268051386304359453740694320253125}{559802981622308320230768057094382747648}\cdot t^{27}-\frac{108974797780430149888775418019735581962181489665396799205935301238265794874103125}{1119605963244616640461536114188765495296}\cdot t^{25}+\frac{2549386537804004855778099370819040775822882272143659485739340965975263975869453125}{4478423852978466561846144456755061981184}\cdot t^{23}-\frac{24028959686704230359088550506384283066223220302842277792262629938058096768449640625}{8956847705956933123692288913510123962368}\cdot t^{21}+\frac{179777184549027139666060554992952824270575504709001982063732967426683447739657203125}{17913695411913866247384577827020247924736}\cdot t^{19}-\frac{1048003963903704293042365536058514114680742944155811152408208696983480003341887828125}{35827390823827732494769155654040495849472}\cdot t^{17}+\frac{2325160652802003418008748829297365593239994870613576063764358981595057462903013421875}{35827390823827732494769155654040495849472}\cdot t^{15}-\frac{7622162975619866312277035946811230184027912829969625156083523048419816081291428359375}{71654781647655464989538311308080991698944}\cdot t^{13}+\frac{17746666155466514026723744495894920855065195002824593383783630128491640609869818359375}{143309563295310929979076622616161983397888}\cdot t^{11}-\frac{27811741018957279363999863037239850894876771471775770157943726393872476369709863359375}{286619126590621859958153245232323966795776}\cdot t^9+\frac{217237152955556046512376453203608096002708611446861484618054916586370313303630440859375}{4585906025449949759330451923717183468732416}\cdot t^7-\frac{117198223380316004658298088500400248878243996139471569518392188126838034087191343671875}{9171812050899899518660903847434366937464832}\cdot t^5+\frac{28280771221338496708447133010255315596321059757763212221343415045076057668256590234375}{18343624101799799037321807694868733874929664}\cdot t^3-\frac{1893555149364347217457371831159728500253929669243317821514530273437289698914793359375}{36687248203599598074643615389737467749859328}\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.