Rule: Q[1, 78]

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^{79}-3081\cdot t^{77}+\frac{4507503}{2}\cdot t^{75}-\frac{4169440275}{4}\cdot t^{73}+\frac{2739322260675}{8}\cdot t^{71}-\frac{1361443163555475}{16}\cdot t^{69}+\frac{532324276950190725}{32}\cdot t^{67}-\frac{168138425190981670425}{64}\cdot t^{65}+\frac{10928997637413808577625}{32}\cdot t^{63}-\frac{2371592487318796461344625}{64}\cdot t^{61}+\frac{434001425179339752426066375}{128}\cdot t^{59}-\frac{67506948952895483309181778875}{256}\cdot t^{57}+\frac{8978424210735099280121176590375}{512}\cdot t^{55}-\frac{1025612304072432494690765172054375}{1024}\cdot t^{53}+\frac{100949553929415141263133886220780625}{2048}\cdot t^{51}-\frac{8580712084000287007366380328766353125}{4096}\cdot t^{49}+\frac{1261364676348042190082857908328653909375}{16384}\cdot t^{47}-\frac{80207953831307859263504082288427933884375}{32768}\cdot t^{45}+\frac{4411437460721932259492724525863536363640625}{65536}\cdot t^{43}-\frac{209659369843784464753785802466040701914078125}{131072}\cdot t^{41}+\frac{8596034163595163054905217901107668778477203125}{262144}\cdot t^{39}-\frac{303317205486857896365941260224799169754838453125}{524288}\cdot t^{37}+\frac{9182239038829425408168949059532556684396473171875}{1048576}\cdot t^{35}-\frac{237540531656674265993935856105298749009387023359375}{2097152}\cdot t^{33}+\frac{2612945848223416925933294417158286239103257256953125}{2097152}\cdot t^{31}-\frac{48600792776955554822359276159144124047320584979328125}{4194304}\cdot t^{29}+\frac{758920071824767509918379466177404398585082980831046875}{8388608}\cdot t^{27}-\frac{9865960933721977628938933060306257181606078750803609375}{16777216}\cdot t^{25}+\frac{105706724289878331738631425646138469802922272330038671875}{33554432}\cdot t^{23}-\frac{922200042942731652754267265119759753797908099982751171875}{67108864}\cdot t^{21}+\frac{6455400300599121569279870855838318276585356699879258203125}{134217728}\cdot t^{19}-\frac{35608821012982251236995416656398465332132128892882359765625}{268435456}\cdot t^{17}+\frac{605349957220698271028922083158773910646246191179000116015625}{2147483648}\cdot t^{15}-\frac{1926113500247676316910206628232462442965328790115000369140625}{4294967296}\cdot t^{13}+\frac{4418730971156433903499885794180355016214577812616765552734375}{8589934592}\cdot t^{11}-\frac{6943720097531538991214106247997700739765765134112060154296875}{17179869184}\cdot t^9+\frac{6943720097531538991214106247997700739765765134112060154296875}{34359738368}\cdot t^7-\frac{3941030325626008616635033275890586906353542373414953060546875}{68719476736}\cdot t^5+\frac{1037113243585791741219745598918575501671984835109198173828125}{137438953472}\cdot t^3-\frac{79777941814291672401518892224505807820921910393015244140625}{274877906944}\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.