Rule: Q[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.

• $P_1$:
  $128\cdot t^7-1344\cdot t^5+3360\cdot t^3-1680\cdot t$
• $P_2$:
  $128\cdot t^{47}-\frac{1887350422390279728983445372691762348864}{30229520413264054439634042230102181}\cdot t^{45}+\frac{139986110711902581735081623026062237646880}{10076506804421351479878014076700727}\cdot t^{43}-\frac{320690575643872609524133462498780134271068880}{171300615675162975157926239303912359}\cdot t^{41}+\frac{29303748332240785203894709012762935281803824200}{171300615675162975157926239303912359}\cdot t^{39}-\frac{1926614639915944247214215346246739110413705698020}{171300615675162975157926239303912359}\cdot t^{37}+\frac{94385505300412890823920448721654604826521342702510}{171300615675162975157926239303912359}\cdot t^{35}-\frac{207122810427720357384657829975682284471027497934275}{10076506804421351479878014076700727}\cdot t^{33}+\frac{5962999741005285706464697698168906685087043778687075}{10076506804421351479878014076700727}\cdot t^{31}-\frac{8612354109922727189430333365015495510050031084635125}{650097213188474289024388004948434}\cdot t^{29}+\frac{300782272004148167874046705376097690137947489909974075}{1300194426376948578048776009896868}\cdot t^{27}-\frac{8189138062693759051448999509464623436456236338396612575}{2600388852753897156097552019793736}\cdot t^{25}+\frac{173118765874163818748986855616207441723023864205122914375}{5200777705507794312195104039587472}\cdot t^{23}-\frac{2820729386463628865148301867302806936702121590561673714375}{10401555411015588624390208079174944}\cdot t^{21}+\frac{35034752813126450939111378713000524003705720064827957215625}{20803110822031177248780416158349888}\cdot t^{19}-\frac{326699583297482540725838206817584755340878846941694105208125}{41606221644062354497560832316699776}\cdot t^{17}+\frac{4482461486906210681369193956276739006145013661027011303938125}{166424886576249417990243329266799104}\cdot t^{15}-\frac{22022629004975606999276595757477413491850117269849694717103125}{332849773152498835980486658533598208}\cdot t^{13}+\frac{74762968223193501667439366939426243898821887981854138786946875}{665699546304997671960973317067196416}\cdot t^{11}-\frac{167032862720640462540482307669067523742848279352080548936359375}{1331399092609995343921946634134392832}\cdot t^9+\frac{229185226256258907389982777205890464948959796456746133861446875}{2662798185219990687843893268268785664}\cdot t^7-\frac{173755859918439226628844803263684297895697102090236708301196875}{5325596370439981375687786536537571328}\cdot t^5+\frac{60451945614242210330039493030950543969613413108851433618953125}{10651192740879962751375573073075142656}\cdot t^3-\frac{6256346681180566489229743524278615609711128802947346644265625}{21302385481759925502751146146150285312}\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.