Rule: Q[1, 64]

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.

• $P_1$:
  $2\cdot t$
• $P_2$:
  $2\cdot t^{65}-2080\cdot t^{63}+1015560\cdot t^{61}-309745800\cdot t^{59}+66246882975\cdot t^{57}-10573002522810\cdot t^{55}+\frac{2616818124395475}{2}\cdot t^{53}-\frac{257569669672640325}{2}\cdot t^{51}+\frac{328401328832616414375}{32}\cdot t^{49}-\frac{5363888370932734768125}{8}\cdot t^{47}+\frac{1159672665795657256868625}{32}\cdot t^{45}-\frac{52185269960804576559088125}{32}\cdot t^{43}+\frac{15707766258202177544285525625}{256}\cdot t^{41}-\frac{247699390994726645890656365625}{128}\cdot t^{39}+\frac{26220749818156063514996623846875}{512}\cdot t^{37}-\frac{582100645963064610032925049400625}{512}\cdot t^{35}+\frac{346349884348023442969590404393371875}{16384}\cdot t^{33}-\frac{672326246087339624588028432057721875}{2048}\cdot t^{31}+\frac{34736856047845880603714802322982296875}{8192}\cdot t^{29}-\frac{371135883037511250660742361661337171875}{8192}\cdot t^{27}+\frac{26053738989233289796384113788625869465625}{65536}\cdot t^{25}-\frac{93049067818690320701371834959378105234375}{32768}\cdot t^{23}+\frac{2140128559829877376131552204065696420390625}{131072}\cdot t^{21}-\frac{9770152120962483673644042670734701049609375}{131072}\cdot t^{19}+\frac{556898670894861569397710432231877959827734375}{2097152}\cdot t^{17}-\frac{378691096208505867190443093917677012682859375}{524288}\cdot t^{15}+\frac{3058658853991778158076655758565852794746171875}{2097152}\cdot t^{13}-\frac{4418062789099235117221836095706231814633359375}{2097152}\cdot t^{11}+\frac{34713350485779704492457283609120392829262109375}{16777216}\cdot t^9-\frac{10773108771448873808003984568347708119426171875}{8388608}\cdot t^7+\frac{15082352280028423331205578395686791367196640625}{33554432}\cdot t^5-\frac{2432637464520713440517028773497869575354296875}{33554432}\cdot t^3+\frac{7297912393562140321551086320493608726062890625}{2147483648}\cdot t$

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.