Rule: Q[1, 82]

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.

• $P_1$:
  $2\cdot t$
• $P_2$:
  $2\cdot t^{83}-3403\cdot t^{81}+2756430\cdot t^{79}-1415426805\cdot t^{77}+\frac{2070769415715}{4}\cdot t^{75}-\frac{1149277025721825}{8}\cdot t^{73}+\frac{251691668633079675}{8}\cdot t^{71}-\frac{89350542364743284625}{16}\cdot t^{69}+\frac{104808186193843872865125}{128}\cdot t^{67}-\frac{25747877741620978100532375}{256}\cdot t^{65}+\frac{334722410641072715306920875}{32}\cdot t^{63}-\frac{59428442543819546635856042625}{64}\cdot t^{61}+\frac{18125674975864961723936093000625}{256}\cdot t^{59}-\frac{2385617683361919193050358086466875}{512}\cdot t^{57}+\frac{135980207951629394003870410928611875}{512}\cdot t^{55}-\frac{13462040587211310006383170681932575625}{1024}\cdot t^{53}+\frac{9275345964588592594398004599851544605625}{16384}\cdot t^{51}-\frac{695650947344144444579850344988865845421875}{32768}\cdot t^{49}+\frac{11362298806621025928137555634818142141890625}{16384}\cdot t^{47}-\frac{646455000524069948858773560065179560809671875}{32768}\cdot t^{45}+\frac{63999045051882924937018582446452776520157515625}{131072}\cdot t^{43}-\frac{2751958937230965772291799045197469390366773171875}{262144}\cdot t^{41}+\frac{51286507466577089392710800387771020456835318203125}{262144}\cdot t^{39}-\frac{1652317479684070575652117525536448963413694382109375}{524288}\cdot t^{37}+\frac{183407240244931833897385045334545834938920076414140625}{4194304}\cdot t^{35}-\frac{4365092317829377646757764078962190871546297818656546875}{8388608}\cdot t^{33}+\frac{11080618960643804795615862661980946058540602155051234375}{2097152}\cdot t^{31}-\frac{190832882099976638146717634734116293230421481559215703125}{4194304}\cdot t^{29}+\frac{5534153580899322506254811407289372503682222965217255390625}{16777216}\cdot t^{27}-\frac{66982341617091799989497889791674818923877940027284711796875}{33554432}\cdot t^{25}+\frac{334911708085458999947489448958374094619389700136423558984375}{33554432}\cdot t^{23}-\frac{2733311682116810547958542922144149868990503036597263239453125}{67108864}\cdot t^{21}+\frac{286997726622265107535647006825135736244002818842712640142578125}{2147483648}\cdot t^{19}-\frac{1487170037951737375411989035366612451446196424912238226193359375}{4294967296}\cdot t^{17}+\frac{1487170037951737375411989035366612451446196424912238226193359375}{2147483648}\cdot t^{15}-\frac{4461510113855212126235967106099837354338589274736714678580078125}{4294967296}\cdot t^{13}+\frac{19333210493372585880355857459765961868800553523859096940513671875}{17179869184}\cdot t^{11}-\frac{28738556138797087119447896223976429804973795778709468425087890625}{34359738368}\cdot t^9+\frac{13613000276272304425001635053462519381303376947809748201357421875}{34359738368}\cdot t^7-\frac{7330077071838933151923957336479818128394126048820633646884765625}{68719476736}\cdot t^5+\frac{7330077071838933151923957336479818128394126048820633646884765625}{549755813888}\cdot t^3-\frac{536347102817482913555411512425352545980058003572241486357421875}{1099511627776}\cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

All rules of Hermite (physicists') type can be downloaded here packed into a single file.