Rule: Q[23, 38]

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.

• $P_1$:
  $8388608\cdot t^{23}-1061158912\cdot t^{21}+55710842880\cdot t^{19}-1587759022080\cdot t^{17}+26991903375360\cdot t^{15}-283414985441280\cdot t^{13}+1842197405368320\cdot t^{11}-7237204092518400\cdot t^9+16283709208166400\cdot t^7-18997660742860800\cdot t^5+9498830371430400\cdot t^3-1295295050649600\cdot t$
• $P_2$:
  $8388608\cdot t^{61}-\frac{2144571648942432664273818040682040512217088}{379487379173538115785382024209093}\cdot t^{59}+\frac{1293295739970957637817486078438857698609987584}{729783421487573299587273123479025}\cdot t^{57}-\frac{1088272710496734744270975999339526330455642865664}{3162394826446150964878183535075775}\cdot t^{55}+\frac{146860562847578481445395423760034006196977500291072}{3162394826446150964878183535075775}\cdot t^{53}-\frac{2930491688183182685304696747803064895383757624508416}{632478965289230192975636707015155}\cdot t^{51}+\frac{74844423269064043702051071325893304298804706228273152}{210826321763076730991878902338385}\cdot t^{49}-\frac{1505263396053138012560932718175152474909654196228882432}{70275440587692243663959634112795}\cdot t^{47}+\frac{72765052955957239609998177673244115016919672105116352512}{70275440587692243663959634112795}\cdot t^{45}-\frac{2852474819065589420382226200904463311118138311248997810176}{70275440587692243663959634112795}\cdot t^{43}+\frac{18289203196620484682345878641460545457853128320161191133184}{14055088117538448732791926822559}\cdot t^{41}-\frac{482205363921002670465274342397609051854044183435214907765760}{14055088117538448732791926822559}\cdot t^{39}+\frac{807065639941810734109431181832609427522426913978277763383808}{1081160624426034517907071294043}\cdot t^{37}-\frac{14514119801994157761523459701792617159061077157916002873256704}{1081160624426034517907071294043}\cdot t^{35}+\frac{215721645606849528692666992807188017816506143311410906879592832}{1081160624426034517907071294043}\cdot t^{33}-\frac{2645479213528267060658040945883891288130823926829320181474727680}{1081160624426034517907071294043}\cdot t^{31}+\frac{26683707912721424302481048963885332449292916300718323170041976320}{1081160624426034517907071294043}\cdot t^{29}-\frac{220321730873713334547586121988791676371785024657104905733030639840}{1081160624426034517907071294043}\cdot t^{27}+\frac{1479564359088989365582461854646619958445100041063864738158502913200}{1081160624426034517907071294043}\cdot t^{25}-\frac{8013706785460377839051303938633729952562298842076242107963250954900}{1081160624426034517907071294043}\cdot t^{23}+\frac{34636066100743851682695877258252001774377294407753940921584733760250}{1081160624426034517907071294043}\cdot t^{21}-\frac{117866348616128760547425755555351705736139355979782517365474788804875}{1081160624426034517907071294043}\cdot t^{19}+\frac{621008289315102283717436307302900297326848383383837702910255036857875}{2162321248852069035814142588086}\cdot t^{17}-\frac{1239493550570826701724094778006617872017147591014944615204082919860125}{2162321248852069035814142588086}\cdot t^{15}+\frac{3645938568684221069169668353839830098247861383048528246388561634133875}{4324642497704138071628285176172}\cdot t^{13}-\frac{3808154861741871138372420610015821121944977257649138276945048744450625}{4324642497704138071628285176172}\cdot t^{11}+\frac{5369368540347360468150581007274043847621474673565124986216377516704375}{8649284995408276143256570352344}\cdot t^9-\frac{18964341089642951574292569777307359762874747521995057012225263510764375}{69194279963266209146052562818752}\cdot t^7+\frac{9271636300008381574681591985582291537096006606691456689128388425284375}{138388559926532418292105125637504}\cdot t^5-\frac{1966286603320798098596118003397128383007297431202945638774951620303125}{276777119853064836584210251275008}\cdot t^3+\frac{91112778854295652373889111602546018731285016284285541680280964478125}{553554239706129673168420502550016}\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.