Rule: Q[6, 51]

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^{57}-\frac{6514780041361137300936536605460467707159453302565302110880}{141049776424247813923944329821556430467928027552521411}\cdot t^{55}+\frac{50155007653442479234768118343995653498126636204300988575802960}{3244144857757699720250719585895797900762344633707992453}\cdot t^{53}-\frac{10352367281442442596197291915017868798635727894607506320704227960}{3244144857757699720250719585895797900762344633707992453}\cdot t^{51}+\frac{1477821916851657182282223530699112490828191964819884861747152967000}{3244144857757699720250719585895797900762344633707992453}\cdot t^{49}-\frac{155113814020583849083762105776340349622253739861027216645280899234100}{3244144857757699720250719585895797900762344633707992453}\cdot t^{47}+\frac{11493956411216032368282012764831124869267160441834469449483229806750}{3001059072856336466466900634501200648253787820266413}\cdot t^{45}-\frac{719902127584264923736197865153077890840881582774994324994260026615125}{3001059072856336466466900634501200648253787820266413}\cdot t^{43}+\frac{143353643781945117787937000243803224216658202573045199773572420983807375}{12004236291425345865867602538004802593015151281065652}\cdot t^{41}-\frac{11471242786205005579627598437124392525793802518321441780352279351646025625}{24008472582850691731735205076009605186030302562131304}\cdot t^{39}+\frac{743177651017558247715804334446564957498101614528989868374099845031600582375}{48016945165701383463470410152019210372060605124262608}\cdot t^{37}-\frac{39154530207761771578621716735483812974780216441291272301623922394790058393125}{96033890331402766926940820304038420744121210248525216}\cdot t^{35}+\frac{420262348396801205945975982360198433369103556536254534898422050651615991558125}{48016945165701383463470410152019210372060605124262608}\cdot t^{33}-\frac{14704203434957061467830891240408928180451687594543958374728420650734471739944375}{96033890331402766926940820304038420744121210248525216}\cdot t^{31}+\frac{418484803102950561996115795067095734865909767943191679281690936465077265694978125}{192067780662805533853881640608076841488242420497050432}\cdot t^{29}-\frac{9652218582470912320755855756794892260076881718337650919641887491212049791444039375}{384135561325611067707763281216153682976484840994100864}\cdot t^{27}+\frac{717630183337755386221706418854208834761992229985824814232015464663210122223781546875}{3073084490604888541662106249729229463811878727952806912}\cdot t^{25}-\frac{10666350011559551998563946657320205835898396395529465834486883506050530110732048328125}{6146168981209777083324212499458458927623757455905613824}\cdot t^{23}+\frac{125485611181715296298573002452157708819520445830743644735223860216845644148424615796875}{12292337962419554166648424998916917855247514911811227648}\cdot t^{21}-\frac{1153126681564151131472715832986689437943163563286093954334336732337994583566983165390625}{24584675924839108333296849997833835710495029823622455296}\cdot t^{19}+\frac{4067934075570645451585046336617662640623291921441540418610236188807416576984915466046875}{24584675924839108333296849997833835710495029823622455296}\cdot t^{17}-\frac{21546465312513618982336644015413546541472071899514552288646310832723086648781282227578125}{49169351849678216666593699995667671420990059647244910592}\cdot t^{15}+\frac{83138580403951064400272298647955616986688779439251556770845990648563055891712762532734375}{98338703699356433333187399991335342841980119294489821184}\cdot t^{13}-\frac{224221228005778647831654896269859882386306754270842177181544186953349641990602161696328125}{196677407398712866666374799982670685683960238588979642368}\cdot t^{11}+\frac{796448568064265826588256552731814562453830339243550428222656975558309740024448022578515625}{786709629594851466665499199930682742735840954355918569472}\cdot t^9-\frac{850091796715687575425240504927023261001213283360958977535183864016280053459031970975359375}{1573419259189702933330998399861365485471681908711837138944}\cdot t^7+\frac{466550268245167084752698356648390805270226131180317092495794897012752493826861516680390625}{3146838518379405866661996799722730970943363817423674277888}\cdot t^5-\frac{95028747902755215175904123448225393698345379376542457130770169160596273441813997034921875}{6293677036758811733323993599445461941886727634847348555776}\cdot t^3+\frac{116885759186313047510708417885054800427177999885459086584111454783871575252818903046875}{786709629594851466665499199930682742735840954355918569472}\cdot t$

Warning: This rule has negative weights!

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.