Rule: Q[2, 3, 58]

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.

• $P_1$:
  $t^2-1$
• $P_2$:
  $t^5-7\cdot t^3+6\cdot t$
• $P_3$:
  $t^{63}-\frac{492244951036495519031005917339353859656122845227156862587749829183341559}{268188556728074217334539756228439247211460559426915984224397571191832}\cdot t^{61}+\frac{181056842712111241122917634668850787980397081671034324323079923626348894041}{114937952883460378857659895526473963090625954040106850381884673367928}\cdot t^{59}-\frac{84574113680665078028708531242201599606496722533051707549613485769486131097849}{100570708773027831500452408585664717704297709785093494084149089196937}\cdot t^{57}+\frac{6003072704453338127610171674452281267968812830169508767328666757942893417233963}{19156325480576729809609982587745660515104325673351141730314112227988}\cdot t^{55}-\frac{1107472062282512187273022728265579892088829115266686192389267062426430288919197505}{12770883653717819873073321725163773676736217115567427820209408151992}\cdot t^{53}+\frac{236387233084824448615367192580653971588805105496929556032139027102727600040747872935}{12770883653717819873073321725163773676736217115567427820209408151992}\cdot t^{51}-\frac{19953492860197876586297548391503644254175211404052993365199123642500787110576611316825}{6385441826858909936536660862581886838368108557783713910104704075996}\cdot t^{49}+\frac{1355345461137853142521937106439230258557726364642797157459547344828627048665885621342475}{3192720913429454968268330431290943419184054278891856955052352037998}\cdot t^{47}-\frac{599886896616351319091567841741532803949363553666406987456354453593773794764542233208617075}{12770883653717819873073321725163773676736217115567427820209408151992}\cdot t^{45}+\frac{54525946932954008600828658894679329863802732024157541649360880083559562919205238821858454625}{12770883653717819873073321725163773676736217115567427820209408151992}\cdot t^{43}-\frac{1023613792447317668308931387008702278121538328400046308292477352972938405811991904027796928875}{3192720913429454968268330431290943419184054278891856955052352037998}\cdot t^{41}+\frac{127455082545295814650642640605518058455467514242548775059779418704052423601097770969819746146375}{6385441826858909936536660862581886838368108557783713910104704075996}\cdot t^{39}-\frac{13180278904538253952006288843253405949370916768295929632309383083984827902648834068842600065554625}{12770883653717819873073321725163773676736217115567427820209408151992}\cdot t^{37}+\frac{566057250861111891201642010372207367910807198229448594303366896632021345891570309581091459205221375}{12770883653717819873073321725163773676736217115567427820209408151992}\cdot t^{35}-\frac{10082568210430102243352370827206489700410278746404866233453436026775389332211383735958804412916254375}{6385441826858909936536660862581886838368108557783713910104704075996}\cdot t^{33}+\frac{74273853649759432410038107701682433596096460302459339815999515531299810098437865036974332767583260000}{1596360456714727484134165215645471709592027139445928477526176018999}\cdot t^{31}-\frac{14420277019847743743920233351369499644261871308720124462120095165915158694463232184133710955021165525625}{12770883653717819873073321725163773676736217115567427820209408151992}\cdot t^{29}+\frac{286551004907065092338270252092648663016951699887440708268170006498059437901300678367689978613116155006875}{12770883653717819873073321725163773676736217115567427820209408151992}\cdot t^{27}-\frac{578395757326799247626836548837535878260243538117368510903337613491383257139073050487787222970325139410000}{1596360456714727484134165215645471709592027139445928477526176018999}\cdot t^{25}+\frac{30069311976321908647206070365453808031621900743887710736372524344012298103715699698568427299641915716484375}{6385441826858909936536660862581886838368108557783713910104704075996}\cdot t^{23}-\frac{621635346825401945171066403345459477517638197365681092268388612873688550682450068902943941462088675536796875}{12770883653717819873073321725163773676736217115567427820209408151992}\cdot t^{21}+\frac{5035412028356950171485966463051207161631888600936214502781963910195502662861900005121734436651922606219328125}{12770883653717819873073321725163773676736217115567427820209408151992}\cdot t^{19}-\frac{15690372647399488891495215725298553804983693266420527075175325928343929392549509739202629885010819674957984375}{6385441826858909936536660862581886838368108557783713910104704075996}\cdot t^{17}+\frac{36758402613548150911526924198037038500987081103343147705579538632535902740673704123886710982316950550794984375}{3192720913429454968268330431290943419184054278891856955052352037998}\cdot t^{15}-\frac{503043489544054392579509144066076861724575759950174064261912931543324934670204724948556199419924676558302765625}{12770883653717819873073321725163773676736217115567427820209408151992}\cdot t^{13}+\frac{1210106144776656129098228163424125017523606575170933911608626685218009034898048451763470641832544215328523421875}{12770883653717819873073321725163773676736217115567427820209408151992}\cdot t^{11}-\frac{486622950079600104639844949344733815393206227280880917089286879966807134199760773359734259560089514441205484375}{3192720913429454968268330431290943419184054278891856955052352037998}\cdot t^9+\frac{976202326485979699469550604609900249537112693513810531540980470307681784360197039145071835699685209092004015625}{6385441826858909936536660862581886838368108557783713910104704075996}\cdot t^7-\frac{1099706733591692942422626261430363835106060116487450861231346821948720354070862110714346086257974672748645421875}{12770883653717819873073321725163773676736217115567427820209408151992}\cdot t^5+\frac{289980129814260404123084633250867520402497739057508471248351922841217660555797014054256991250265836128618828125}{12770883653717819873073321725163773676736217115567427820209408151992}\cdot t^3-\frac{11685665056427044973903075599360722831692665676964142599229064574494868489447326295943260462326120957898515625}{6385441826858909936536660862581886838368108557783713910104704075996}\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.