Rule: Q[9, 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.

• $P_1$:
  $512\cdot t^9-9216\cdot t^7+48384\cdot t^5-80640\cdot t^3+30240\cdot t$
• $P_2$:
  $512\cdot t^{55}-\frac{140293532295767141014176054278771611745843240147200}{424222306338984413743764211130890177598635909}\cdot t^{53}+\frac{209237422360563337756954662856384164411352941434183808}{2121111531694922068718821055654450887993179545}\cdot t^{51}-\frac{1493964980926637834721580582195518080783651576335488447424}{82723349736101960680034021170523584631734002255}\cdot t^{49}+\frac{3575879747070907822408092080704234583528559399862144628322752}{1571743644985937252920646402239948108002946042845}\cdot t^{47}-\frac{329397917118237244744535435004102609822964297885750074358644064}{1571743644985937252920646402239948108002946042845}\cdot t^{45}+\frac{1534509867924273493137632961090898282907836597980811903326738000}{104782909665729150194709760149329873866863069523}\cdot t^{43}-\frac{2031534453768609438348146517797099277970744792609294824240428136}{2555680723554369516944140491447070094313733403}\cdot t^{41}+\frac{6693430311630791120981478486688407789733150485896632590296313738}{196590824888797655149549268572851545716441031}\cdot t^{39}-\frac{12030853034564456381535729173056919108493857198170199319698588979}{10346885520463034481555224661729028721917949}\cdot t^{37}+\frac{659441636556025226755935615625313666381847770135903727834786641511}{20693771040926068963110449323458057443835898}\cdot t^{35}-\frac{29107649598758034685756517797538230078531021613251452837880072382175}{41387542081852137926220898646916114887671796}\cdot t^{33}+\frac{258904741995070069598993212990104160190640672490216956531768319108005}{20693771040926068963110449323458057443835898}\cdot t^{31}-\frac{7415491353310673916932250375307742074782593298939955249372152187552065}{41387542081852137926220898646916114887671796}\cdot t^{29}+\frac{170404593010334499653331628393399861304676250751871238088710279860502185}{82775084163704275852441797293832229775343592}\cdot t^{27}-\frac{3124555226274321772678795449650505609288083425980602838244934073638057865}{165550168327408551704883594587664459550687184}\cdot t^{25}+\frac{181461108307881126235189760849055514855632429569960814997524040745695186875}{1324401346619268413639068756701315676405497472}\cdot t^{23}-\frac{2065107696196375368397229868808347021013926686681436381447136670688389682375}{2648802693238536827278137513402631352810994944}\cdot t^{21}+\frac{18183543082252591704870030244486982951372684505010968593658831177039564775875}{5297605386477073654556275026805262705621989888}\cdot t^{19}-\frac{121851965967107644363757590669590336845829576487440911003781649629747181072875}{10595210772954147309112550053610525411243979776}\cdot t^{17}+\frac{304296515283395207602127438060143278799973164847478644731387580472678891321375}{10595210772954147309112550053610525411243979776}\cdot t^{15}-\frac{1102827737169257912158081229578971211399088223882982541933352132146000331871875}{21190421545908294618225100107221050822487959552}\cdot t^{13}+\frac{2800745701728447084960542423893442487673189854787038555318310186815169981981875}{42380843091816589236450200214442101644975919104}\cdot t^{11}-\frac{4756159846198702694006459868430830144183580116748068703376432124000268568851875}{84761686183633178472900400428884203289951838208}\cdot t^9+\frac{10116011610869745103850621991344275184756764863832288584166625597568306853430625}{339046744734532713891601601715536813159807352832}\cdot t^7-\frac{6103426311970099575963446885908647339031125602766122565194216918218156309963125}{678093489469065427783203203431073626319614705664}\cdot t^5+\frac{1758588766897228875833203668080943799103125286648268616785672533262182602640625}{1356186978938130855566406406862147252639229411328}\cdot t^3-\frac{160333823114756615977209943896885593936798847647557626187042036534221960665625}{2712373957876261711132812813724294505278458822656}\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.