Rule: Q[8, 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.

• $P_1$:
  $256\cdot t^8-3584\cdot t^6+13440\cdot t^4-13440\cdot t^2+1680$
• $P_2$:
  $256\cdot t^{48}-\frac{116669712831346372992836758764227400444366848}{947397510533097832003392609306155659087}\cdot t^{46}+\frac{435084524161696110401045486350891651804301510400}{16105757679062663144057674358204646204479}\cdot t^{44}-\frac{635604650535370206575347977485385973885137610874880}{177163334469689294584634417940251108249269}\cdot t^{42}+\frac{57223416813884672582944894703208408083882509995032880}{177163334469689294584634417940251108249269}\cdot t^{40}-\frac{218004290133502978001944110393633521000554664132653920}{10421372615864076152037318702367712249957}\cdot t^{38}+\frac{178839975824488728947067326088846904935748915382202037560}{177163334469689294584634417940251108249269}\cdot t^{36}-\frac{6572365651279585092838100193152317521648106474057356681000}{177163334469689294584634417940251108249269}\cdot t^{34}+\frac{997124310869871746738357969768965794161172876188818066200}{947397510533097832003392609306155659087}\cdot t^{32}-\frac{22011800758171852220363272695477679331412324614451140200200}{947397510533097832003392609306155659087}\cdot t^{30}+\frac{379442744045677504525146642788638709590042706113140696864600}{947397510533097832003392609306155659087}\cdot t^{28}-\frac{5107619805592824747321175506832743270431090095452933245049150}{947397510533097832003392609306155659087}\cdot t^{26}+\frac{428121114340594304078176908388898111185752775551421390379953125}{7579180084264782656027140874449245272696}\cdot t^{24}-\frac{1734702523795553891073147864750198733055409774731418042427794375}{3789590042132391328013570437224622636348}\cdot t^{22}+\frac{43073715628268288814177755528185725050905235323864494634524886875}{15158360168529565312054281748898490545392}\cdot t^{20}-\frac{202094987224605760092958468587148401904202725273661459257048310625}{15158360168529565312054281748898490545392}\cdot t^{18}+\frac{11262269130152386726031375567264209134435722638830546359945960664375}{242533762696473044992868507982375848726272}\cdot t^{16}-\frac{3553944090767884750047897484920530918737670973472860699390352171875}{30316720337059130624108563497796981090784}\cdot t^{14}+\frac{50382079932029806564463540258305773491286150083714937233550987253125}{242533762696473044992868507982375848726272}\cdot t^{12}-\frac{29988306519536273470785147104034426865062187916989405158446399071875}{121266881348236522496434253991187924363136}\cdot t^{10}+\frac{721238334279968779743512967357714511872101366322596950294966294978125}{3880540203143568719885896127718013579620352}\cdot t^8-\frac{156152620935443136879945476894298152967869315040231264212792772815625}{1940270101571784359942948063859006789810176}\cdot t^6+\frac{135010264765804844995359649047893928802054988567049286263306028828125}{7761080406287137439771792255436027159240704}\cdot t^4-\frac{11272255353202649977953552434558552399483668959323303074553600484375}{7761080406287137439771792255436027159240704}\cdot t^2+\frac{683631594066895310631927249899783673562538134223086406987696390625}{31044321625148549759087169021744108636962816}$

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.