Rule: Q[1, 68]

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^{69}-2346\cdot t^{67}+\frac{2593503}{2}\cdot t^{65}-449540520\cdot t^{63}+109744079445\cdot t^{61}-20083166538435\cdot t^{59}+\frac{11454099315754095}{4}\cdot t^{57}-\frac{652883660997983415}{2}\cdot t^{55}+\frac{969532236582005371275}{32}\cdot t^{53}-\frac{74223079000555744534275}{32}\cdot t^{51}+\frac{18926885145141714856240125}{128}\cdot t^{49}-\frac{252932010575984734897027125}{32}\cdot t^{47}+\frac{91139834477546499474562107375}{256}\cdot t^{45}-\frac{3470324466645039787685249473125}{256}\cdot t^{43}+\frac{447671856197210132611397182033125}{1024}\cdot t^{41}-\frac{6118182034695205145689094821119375}{512}\cdot t^{39}+\frac{4533572887709147012955619262449456875}{16384}\cdot t^{37}-\frac{88804692447479173842013012611509949375}{16384}\cdot t^{35}+\frac{5870976889583345381777526944872046653125}{65536}\cdot t^{33}-\frac{10196959860855284084139915220040923134375}{8192}\cdot t^{31}+\frac{948317267059541419825012115463805851496875}{65536}\cdot t^{29}-\frac{9167066914908900391641783782816789897803125}{65536}\cdot t^{27}+\frac{292512771557547639769660555251699386738990625}{262144}\cdot t^{25}-\frac{953845994209394477509762680168584956757578125}{131072}\cdot t^{23}+\frac{80441012178325600936656652694217331353222421875}{2097152}\cdot t^{21}-\frac{337852251148967523933957941315712791683534171875}{2097152}\cdot t^{19}+\frac{4444056534344111276362062151152837490606487953125}{8388608}\cdot t^{17}-\frac{2798109669772218211042779872948082864455936859375}{2097152}\cdot t^{15}+\frac{41971645046583273165641698094221242966839052890625}{16777216}\cdot t^{13}-\frac{56444626097129229429656076747400981920921484921875}{16777216}\cdot t^{11}+\frac{206963629022807174575405614740470267043378778046875}{67108864}\cdot t^9-\frac{60086214877589179715440339763362335593239000078125}{33554432}\cdot t^7+\frac{1261810512429372774024247135030609047458019001640625}{2147483648}\cdot t^5-\frac{191183410974147390003673808337971067796669545703125}{2147483648}\cdot t^3+\frac{33738248995437774706530672059641953140588743359375}{8589934592}\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.