Rule: Q[42]

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.

• $P_1$:
  $\frac{1}{1405006117752879898543142606244511569936384000000000}\cdot t^{42}-\frac{1}{796488728884852550194525286986684563456000000000}\cdot t^{41}+\frac{41}{38853108726090368302171965218862661632000000000}\cdot t^{40}-\frac{41}{72849578861419440566572434785367490560000000}\cdot t^{39}+\frac{41}{191583376361392348630039276227133440000000}\cdot t^{38}-\frac{41}{663377341971580154536147078348800000000}\cdot t^{37}+\frac{1517}{107574704103499484519375201894400000000}\cdot t^{36}-\frac{1517}{581036210435568203422551244800000000}\cdot t^{35}+\frac{1517}{3794522190599629083575844864000000}\cdot t^{34}-\frac{1517}{29542127781485001515728896000000}\cdot t^{33}+\frac{1517}{271277573751010114928640000000}\cdot t^{32}-\frac{1517}{2914114561778428968960000000}\cdot t^{31}+\frac{47027}{1128044346494875729920000000}\cdot t^{30}-\frac{47027}{16293973893814871654400000}\cdot t^{29}+\frac{1363783}{7866056362531317350400000}\cdot t^{28}-\frac{1363783}{150498527344349184000000}\cdot t^{27}+\frac{1363783}{3303122685198336000000}\cdot t^{26}-\frac{1363783}{83066694746112000000}\cdot t^{25}+\frac{1363783}{2392320808688025600}\cdot t^{24}-\frac{1363783}{78913360008806400}\cdot t^{23}+\frac{31367009}{68620313051136000}\cdot t^{22}-\frac{31367009}{2977327632384000}\cdot t^{21}+\frac{31367009}{148528816128000}\cdot t^{20}-\frac{1363783}{371322040320}\cdot t^{19}+\frac{25911877}{469038366720}\cdot t^{18}-\frac{25911877}{36191232000}\cdot t^{17}+\frac{440501909}{55351296000}\cdot t^{16}-\frac{440501909}{5837832000}\cdot t^{15}+\frac{440501909}{726485760}\cdot t^{14}-\frac{15189721}{3706560}\cdot t^{13}+\frac{197466373}{8553600}\cdot t^{12}-\frac{6369883}{59400}\cdot t^{11}+\frac{70068713}{172800}\cdot t^{10}-\frac{6369883}{5184}\cdot t^9+\frac{374699}{128}\cdot t^8-\frac{374699}{70}\cdot t^7+\frac{2622893}{360}\cdot t^6-\frac{70889}{10}\cdot t^5+\frac{18655}{4}\cdot t^4-\frac{5740}{3}\cdot t^3+\frac{861}{2}\cdot t^2-42\cdot t+1$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

All rules of Laguerre type can be downloaded here packed into a single file.