Rule: Q[40]

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.

• $P_1$:
  $\frac{1}{815915283247897734345611269596115894272000000000}\cdot t^{40}-\frac{1}{509947052029936083966007043497572433920000000}\cdot t^{39}+\frac{1}{670541817264873220205137466794967040000000}\cdot t^{38}-\frac{1}{1393092418140318324525908864532480000000}\cdot t^{37}+\frac{37}{150604585744899278327125282652160000000}\cdot t^{36}-\frac{37}{581036210435568203422551244800000000}\cdot t^{35}+\frac{37}{2845891642949721812681883648000000}\cdot t^{34}-\frac{37}{17232907872532917550841856000000}\cdot t^{33}+\frac{37}{126596201083804720300032000000}\cdot t^{32}-\frac{37}{1112661923588127424512000000}\cdot t^{31}+\frac{1147}{358923201157460459520000000}\cdot t^{30}-\frac{1147}{4386839125257850060800000}\cdot t^{29}+\frac{33263}{1815243775968765542400000}\cdot t^{28}-\frac{33263}{30099705468869836800000}\cdot t^{27}+\frac{33263}{578046469909708800000}\cdot t^{26}-\frac{33263}{12826474924032000000}\cdot t^{25}+\frac{33263}{328357758055219200}\cdot t^{24}-\frac{33263}{9691114387046400}\cdot t^{23}+\frac{765049}{7584350389862400}\cdot t^{22}-\frac{765049}{297732763238400}\cdot t^{21}+\frac{765049}{13502619648000}\cdot t^{20}-\frac{765049}{708887531520}\cdot t^{19}+\frac{14535931}{820817141760}\cdot t^{18}-\frac{631997}{2533386240}\cdot t^{17}+\frac{10743949}{3576545280}\cdot t^{16}-\frac{10743949}{349272000}\cdot t^{15}+\frac{10743949}{40360320}\cdot t^{14}-\frac{10743949}{5559840}\cdot t^{13}+\frac{139671337}{11975040}\cdot t^{12}-\frac{4816253}{83160}\cdot t^{11}+\frac{52978783}{226800}\cdot t^{10}-\frac{1708993}{2268}\cdot t^9+\frac{1708993}{896}\cdot t^8-\frac{155363}{42}\cdot t^7+\frac{63973}{12}\cdot t^6-\frac{27417}{5}\cdot t^5+\frac{45695}{12}\cdot t^4-\frac{4940}{3}\cdot t^3+390\cdot t^2-40\cdot t+1$

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.