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.

• $P_1$:
  $t^6-15\cdot t^4+45\cdot t^2-15$
• $P_2$:
  $t^{44}-\frac{8169671914544901765548784855756271}{6237269475162519549492670996882}\cdot t^{42}+\frac{47424251396867212726290577804061033571}{68609964226787715044419380965702}\cdot t^{40}-\frac{112919110130118498011861054921283033822309}{548879713814301720355355047725616}\cdot t^{38}+\frac{21719724782242313079815979517210438689793227}{548879713814301720355355047725616}\cdot t^{36}-\frac{2899101136241919599566065986725829073661126065}{548879713814301720355355047725616}\cdot t^{34}+\frac{1497026984888819981502970609165505867307125745}{2935185635370597435055374586768}\cdot t^{32}-\frac{26817773327604436570445694419172064303915812615}{733796408842649358763843646692}\cdot t^{30}+\frac{1448023092304841997526823050146410854081242170985}{733796408842649358763843646692}\cdot t^{28}-\frac{59404678947089084184562248874557264221400922944555}{733796408842649358763843646692}\cdot t^{26}+\frac{1856888449049577745126270705067093149373484829706625}{733796408842649358763843646692}\cdot t^{24}-\frac{88288990938356695854548792106339979372329214487990625}{1467592817685298717527687293384}\cdot t^{22}+\frac{1586417664455318552426825593593651870741174231733785375}{1467592817685298717527687293384}\cdot t^{20}-\frac{21313604803439128081776466656955682464438296257363125125}{1467592817685298717527687293384}\cdot t^{18}+\frac{210707853844910341423611722495707760957769378454732740375}{1467592817685298717527687293384}\cdot t^{16}-\frac{749474841562407784531744906046338205925851033873299546875}{733796408842649358763843646692}\cdot t^{14}+\frac{3720665384520214581219915081511578539655734624931530960625}{733796408842649358763843646692}\cdot t^{12}-\frac{12354238245653042049691566864397781765023219063457308640625}{733796408842649358763843646692}\cdot t^{10}+\frac{25832844190032984712176786706137598740806263301939527516875}{733796408842649358763843646692}\cdot t^8-\frac{124346529587485208295090812328417378694838066300050546524375}{2935185635370597435055374586768}\cdot t^6+\frac{74322223122432879869658948736530461266170614855574167465625}{2935185635370597435055374586768}\cdot t^4-\frac{16576034493817407424360705889253055399644218443533254596875}{2935185635370597435055374586768}\cdot t^2+\frac{583926872127114303989168714956303789022526093085681115625}{2935185635370597435055374586768}$

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.