Rule: Q[6, 38]

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^{44}-\frac{130714750632718428248780557692100336}{3118634737581259774746335498441}\cdot t^{42}+\frac{379394011174937701810324622432488268568}{34304982113393857522209690482851}\cdot t^{40}-\frac{112919110130118498011861054921283033822309}{68609964226787715044419380965702}\cdot t^{38}+\frac{21719724782242313079815979517210438689793227}{137219928453575430088838761931404}\cdot t^{36}-\frac{2899101136241919599566065986725829073661126065}{274439856907150860177677523862808}\cdot t^{34}+\frac{1497026984888819981502970609165505867307125745}{2935185635370597435055374586768}\cdot t^{32}-\frac{26817773327604436570445694419172064303915812615}{1467592817685298717527687293384}\cdot t^{30}+\frac{1448023092304841997526823050146410854081242170985}{2935185635370597435055374586768}\cdot t^{28}-\frac{59404678947089084184562248874557264221400922944555}{5870371270741194870110749173536}\cdot t^{26}+\frac{1856888449049577745126270705067093149373484829706625}{11740742541482389740221498347072}\cdot t^{24}-\frac{88288990938356695854548792106339979372329214487990625}{46962970165929558960885993388288}\cdot t^{22}+\frac{1586417664455318552426825593593651870741174231733785375}{93925940331859117921771986776576}\cdot t^{20}-\frac{21313604803439128081776466656955682464438296257363125125}{187851880663718235843543973553152}\cdot t^{18}+\frac{210707853844910341423611722495707760957769378454732740375}{375703761327436471687087947106304}\cdot t^{16}-\frac{749474841562407784531744906046338205925851033873299546875}{375703761327436471687087947106304}\cdot t^{14}+\frac{3720665384520214581219915081511578539655734624931530960625}{751407522654872943374175894212608}\cdot t^{12}-\frac{12354238245653042049691566864397781765023219063457308640625}{1502815045309745886748351788425216}\cdot t^{10}+\frac{25832844190032984712176786706137598740806263301939527516875}{3005630090619491773496703576850432}\cdot t^8-\frac{124346529587485208295090812328417378694838066300050546524375}{24045040724955934187973628614803456}\cdot t^6+\frac{74322223122432879869658948736530461266170614855574167465625}{48090081449911868375947257229606912}\cdot t^4-\frac{16576034493817407424360705889253055399644218443533254596875}{96180162899823736751894514459213824}\cdot t^2+\frac{583926872127114303989168714956303789022526093085681115625}{192360325799647473503789028918427648}$

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.