Rule: Q[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.

• $P_1$:
  $\frac{1}{523022617466601111760007224100074291200000000}\cdot t^{38}-\frac{1}{362204028716482764376736304778444800000000}\cdot t^{37}+\frac{37}{19578596146836906182526286744780800000000}\cdot t^{36}-\frac{37}{45320824413974319866958997094400000000}\cdot t^{35}+\frac{37}{147986365433385534259457949696000000}\cdot t^{34}-\frac{37}{640079435265508366174126080000000}\cdot t^{33}+\frac{37}{3526608458763131494072320000000}\cdot t^{32}-\frac{37}{24107675011076094197760000000}\cdot t^{31}+\frac{1147}{6221335486729314631680000000}\cdot t^{30}-\frac{1147}{62213354867293146316800000}\cdot t^{29}+\frac{33263}{21452880988721774592000000}\cdot t^{28}-\frac{33263}{300997054688698368000000}\cdot t^{27}+\frac{33263}{4954684027797504000000}\cdot t^{26}-\frac{33263}{95282385149952000000}\cdot t^{25}+\frac{33263}{2134325427358924800}\cdot t^{24}-\frac{33263}{55581391337472000}\cdot t^{23}+\frac{765049}{38665315713024000}\cdot t^{22}-\frac{765049}{1358079270912000}\cdot t^{21}+\frac{765049}{55431806976000}\cdot t^{20}-\frac{765049}{2633010831360}\cdot t^{19}+\frac{14535931}{2771590348800}\cdot t^{18}-\frac{14535931}{179640115200}\cdot t^{17}+\frac{247110827}{232475443200}\cdot t^{16}-\frac{10743949}{908107200}\cdot t^{15}+\frac{10743949}{96864768}\cdot t^{14}-\frac{10743949}{12355200}\cdot t^{13}+\frac{10743949}{1900800}\cdot t^{12}-\frac{10743949}{356400}\cdot t^{11}+\frac{118183439}{907200}\cdot t^{10}-\frac{4075291}{9072}\cdot t^9+\frac{4075291}{3360}\cdot t^8-\frac{262922}{105}\cdot t^7+\frac{920227}{240}\cdot t^6-\frac{83657}{20}\cdot t^5+\frac{24605}{8}\cdot t^4-1406\cdot t^3+\frac{703}{2}\cdot t^2-38\cdot t+1$

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.