Rule: Q[4, 47]

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^{51}-\frac{376815643136787275887745586686231787907}{317748388298858572428944674243562367}\cdot t^{49}+\frac{2945948386932010065409124300907352973930306}{4554393565616972871481540330824393927}\cdot t^{47}-\frac{981860515611299147220087180412900915939810210}{4554393565616972871481540330824393927}\cdot t^{45}+\frac{6790190608767327850241624561592601349173503520}{138011926230817359741864858509830119}\cdot t^{43}-\frac{8736190037024113916057498768165516791290005920}{1069859893262150075518332236510311}\cdot t^{41}+\frac{1093238345649654795805707100486221524376939058070}{1069859893262150075518332236510311}\cdot t^{39}-\frac{105546655908671538598602175816854375201605687084710}{1069859893262150075518332236510311}\cdot t^{37}+\frac{7979213950661897191165809599013906222401489040541575}{1069859893262150075518332236510311}\cdot t^{35}-\frac{476769836949434110547906499296541061656270694625979675}{1069859893262150075518332236510311}\cdot t^{33}+\frac{22633660795207107498576626455724725930201094251646363700}{1069859893262150075518332236510311}\cdot t^{31}-\frac{855321692283887378073680754753216023566313922610998299700}{1069859893262150075518332236510311}\cdot t^{29}+\frac{886381583482698842221589387923358875089365718439594493400}{36891720457315519845459732293459}\cdot t^{27}-\frac{21107785295616349636113285098542965842732914602412370307000}{36891720457315519845459732293459}\cdot t^{25}+\frac{395766019964847752093829828183495715463550196625922929917500}{36891720457315519845459732293459}\cdot t^{23}-\frac{5788708549360591137955923190528245204028747148457244427257500}{36891720457315519845459732293459}\cdot t^{21}+\frac{65222347617998821284012137170898757092865908281506615135635625}{36891720457315519845459732293459}\cdot t^{19}-\frac{556749307831863080848805347709430861476545790676800025452713125}{36891720457315519845459732293459}\cdot t^{17}+\frac{3523192498605688239929187322334107500646952781076726975525931250}{36891720457315519845459732293459}\cdot t^{15}-\frac{16064032548030960894944954400556341788983215384989880289241231250}{36891720457315519845459732293459}\cdot t^{13}+\frac{50809200490630472438918972819431726344979998151816346190284925000}{36891720457315519845459732293459}\cdot t^{11}-\frac{105842237191660654380379990671143572410601517075604153524857425000}{36891720457315519845459732293459}\cdot t^9+\frac{134826844961550731338285840207413937299981473828080042029447993750}{36891720457315519845459732293459}\cdot t^7-\frac{93719427149152737014272572861258721410257862329733366630834843750}{36891720457315519845459732293459}\cdot t^5+\frac{29160749845685108583966455882163671562427420289832882376140140625}{36891720457315519845459732293459}\cdot t^3-\frac{2595094446405392360052261328293793297238694020944356318651328125}{36891720457315519845459732293459}\cdot t$

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.