Rule: Q[20, 29]

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.

• $P_1$:
  $1048576\cdot t^{20}-99614720\cdot t^{18}+3810263040\cdot t^{16}-76205260800\cdot t^{14}+866834841600\cdot t^{12}-5721109954560\cdot t^{10}+21454162329600\cdot t^8-42908324659200\cdot t^6+40226554368000\cdot t^4-13408851456000\cdot t^2+670442572800$
• $P_2$:
  $1048576\cdot t^{49}-\frac{3123904189828687122124488708471652352}{7221058742728048922645934429}\cdot t^{47}+\frac{587755166720981397224418323623502675968}{7221058742728048922645934429}\cdot t^{45}-\frac{7443444051020270885878707046874507509760}{802339860303116546960659381}\cdot t^{43}+\frac{575855177548463640755062859415539425607680}{802339860303116546960659381}\cdot t^{41}-\frac{32113687037077783688951055856064213974876160}{802339860303116546960659381}\cdot t^{39}+\frac{1338260970426397677786559580610542031420948480}{802339860303116546960659381}\cdot t^{37}-\frac{42637647969184886423511550952224093448897617920}{802339860303116546960659381}\cdot t^{35}+\frac{1054005114430135688713371706127946256298652364800}{802339860303116546960659381}\cdot t^{33}-\frac{20401734747460542906044286454551692953451092070400}{802339860303116546960659381}\cdot t^{31}+\frac{310768252643210235182265743648751825169839353548800}{802339860303116546960659381}\cdot t^{29}-\frac{3731218588576951363322371492201085517579720020198400}{802339860303116546960659381}\cdot t^{27}+\frac{35262043370581562964796644728288967797263033799961600}{802339860303116546960659381}\cdot t^{25}-\frac{261190075765628609159137649722954494382736333748960000}{802339860303116546960659381}\cdot t^{23}+\frac{1505405876275264615240614022960607152414638372120480000}{802339860303116546960659381}\cdot t^{21}-\frac{6680567713523293792357951596625940795079501225884760000}{802339860303116546960659381}\cdot t^{19}+\frac{22497940286990404129407828001624780906570439166064830000}{802339860303116546960659381}\cdot t^{17}-\frac{56389665498854130051283982725548599765694844937636145000}{802339860303116546960659381}\cdot t^{15}+\frac{102488777827481494517221106589337585383598624734533325000}{802339860303116546960659381}\cdot t^{13}-\frac{130375505904698264926857613231447937060673955839627131250}{802339860303116546960659381}\cdot t^{11}+\frac{110445671954530667118754169307541411568974269524039231250}{802339860303116546960659381}\cdot t^9-\frac{115751225666324556011788178195976064045077985823870184375}{1604679720606233093921318762}\cdot t^7+\frac{33346060815891923295392075423630956708138902235074065625}{1604679720606233093921318762}\cdot t^5-\frac{17162252197169927508468063833962649263473437775233296875}{6418718882424932375685275048}\cdot t^3+\frac{1279859128938081913908961497320531987031420297621890625}{12837437764849864751370550096}\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.