Rule: Q[4, 7, 40]

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.

• $P_1$:
  $t^4-6\cdot t^2+3$
• $P_2$:
  $t^{11}-41\cdot t^9+528\cdot t^7-2520\cdot t^5+4095\cdot t^3-1575\cdot t$
• $P_3$:
  $t^{51}-\frac{3748164888323388940709113950537899378550142119016790958881879731182326663}{3452008873983076440048795220156472902343624860042187456485826643003883}\cdot t^{49}+\frac{1867662153975143239126747310170663868771959483410615928428973830356217307794}{3452008873983076440048795220156472902343624860042187456485826643003883}\cdot t^{47}-\frac{9645462820748284348900674079458197937323782590077354798784549939181641230476050}{58684150857712299480829518742660039339841622620717186760259052931066011}\cdot t^{45}+\frac{2001898753310817709785174891898277834109774058030504081096443704561401313265247080}{58684150857712299480829518742660039339841622620717186760259052931066011}\cdot t^{43}-\frac{301495864114617411182657266311208860481891245837484999425344668122234940927438190520}{58684150857712299480829518742660039339841622620717186760259052931066011}\cdot t^{41}+\frac{34162742987448473160452058187537035434975171414210965748253950046688939464560673180870}{58684150857712299480829518742660039339841622620717186760259052931066011}\cdot t^{39}-\frac{2980479209522555112568047762601975998496108535260758513214115053577363160228980307999510}{58684150857712299480829518742660039339841622620717186760259052931066011}\cdot t^{37}+\frac{203243452789597030050691503467992173492402919793280337313954326655047117550344679666447475}{58684150857712299480829518742660039339841622620717186760259052931066011}\cdot t^{35}-\frac{643377652424242744387387388894962754374675047510034930117480234163207897415365701165043775}{3452008873983076440048795220156472902343624860042187456485826643003883}\cdot t^{33}+\frac{27476852496223251337374246741554493458490364589651131042332274942030700952491573994309494100}{3452008873983076440048795220156472902343624860042187456485826643003883}\cdot t^{31}-\frac{933531118257148004783066320539544069549443692392686586932870741415613564624324868613343318100}{3452008873983076440048795220156472902343624860042187456485826643003883}\cdot t^{29}+\frac{25224924891544866827046731464469060076270604108124767856977137480111782132819024041339399069800}{3452008873983076440048795220156472902343624860042187456485826643003883}\cdot t^{27}-\frac{540572664481302913661416719888677065320999199904967076593093965964937508243355635919048838521000}{3452008873983076440048795220156472902343624860042187456485826643003883}\cdot t^{25}+\frac{9138695881946375161619832694992698888634200976142435902867608043803253288338973769910923142347500}{3452008873983076440048795220156472902343624860042187456485826643003883}\cdot t^{23}-\frac{120894310319415214830795787647419658936386667341183294392092337107478965468164646101075288430727500}{3452008873983076440048795220156472902343624860042187456485826643003883}\cdot t^{21}+\frac{1237392422315911944795478818802237878077863954693368415553287163649238015212293309914139623933430625}{3452008873983076440048795220156472902343624860042187456485826643003883}\cdot t^{19}-\frac{9650442168240241803482983592206329602512174607906942710175573206008188295616586249862587671322923125}{3452008873983076440048795220156472902343624860042187456485826643003883}\cdot t^{17}+\frac{56186933988559690605858199031965034289830650681546059114007122991848499684817384020794127988923256250}{3452008873983076440048795220156472902343624860042187456485826643003883}\cdot t^{15}-\frac{237599316110131742693749828729981458340494888994263260839926796436216323799769522661436735149756556250}{3452008873983076440048795220156472902343624860042187456485826643003883}\cdot t^{13}+\frac{703070499574945141615546249627729890048730702161076632050583047324635659820693002469622830900063350000}{3452008873983076440048795220156472902343624860042187456485826643003883}\cdot t^{11}-\frac{1382674183315719054388050695773791533962867847426065313660270927979230644844785148711961983089613100000}{3452008873983076440048795220156472902343624860042187456485826643003883}\cdot t^9+\frac{1679000703533775438654389550798169606460619949155161151061918041426243802967269835825038315438997268750}{3452008873983076440048795220156472902343624860042187456485826643003883}\cdot t^7-\frac{1126401850311081012239995453983557825750585052570062168168090712179077916770482599613086059692053718750}{3452008873983076440048795220156472902343624860042187456485826643003883}\cdot t^5+\frac{345717572934617183295563704991174356691094770989938268138052910489820546883088943143102889450063640625}{3452008873983076440048795220156472902343624860042187456485826643003883}\cdot t^3-\frac{31800727012789693990202343057044898831806179800030850595352023832416349573784452196817352698884453125}{3452008873983076440048795220156472902343624860042187456485826643003883}\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 (probabilists') type can be downloaded here packed into a single file.