Rule: Q[22, 37]

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.

• $P_1$:
  $4194304\cdot t^{22}-484442112\cdot t^{20}+23011000320\cdot t^{18}-586780508160\cdot t^{16}+8801707622400\cdot t^{14}-80095539363840\cdot t^{12}+440525466501120\cdot t^{10}-1415974713753600\cdot t^8+2477955749068800\cdot t^6-2064963124224000\cdot t^4+619488937267200\cdot t^2-28158588057600$
• $P_2$:
  $4194304\cdot t^{59}-\frac{279325036772780096144295912500424081408}{104779331696056756994688859075}\cdot t^{57}+\frac{82482997721619777113631780878544998498304}{104779331696056756994688859075}\cdot t^{55}-\frac{69235346295860368108655627321195723118870528}{481984925801861082175568751745}\cdot t^{53}+\frac{8759644347745647732383011942222007803433582592}{481984925801861082175568751745}\cdot t^{51}-\frac{163460527630173756758876412787239877131542003712}{96396985160372216435113750349}\cdot t^{49}+\frac{58397786134090882530654704072156152917152736411648}{481984925801861082175568751745}\cdot t^{47}-\frac{3275610035450479204757118787191826306265735393869824}{481984925801861082175568751745}\cdot t^{45}+\frac{29339333176022379181695613424311555068498507047043072}{96396985160372216435113750349}\cdot t^{43}-\frac{1061428330441921189167091916311683274024380692254359552}{96396985160372216435113750349}\cdot t^{41}+\frac{2405247767161080175758202152659787414911216818208716800}{7415152704644016648854903873}\cdot t^{39}-\frac{57992530227424766665977910422336953294249007645253395456}{7415152704644016648854903873}\cdot t^{37}+\frac{1147673738387699611530435806970025964213992662043416150528}{7415152704644016648854903873}\cdot t^{35}-\frac{18658881013263940801186840040181235492170333270206403982080}{7415152704644016648854903873}\cdot t^{33}+\frac{248997243169937666526454926082986966454550396951718298022400}{7415152704644016648854903873}\cdot t^{31}-\frac{2720416755167107848449122065776029593220809902561944886419200}{7415152704644016648854903873}\cdot t^{29}+\frac{24230486942202833887165428416928360435521302553537339335867200}{7415152704644016648854903873}\cdot t^{27}-\frac{174883076366786838494338139254312375078231943780097850234543200}{7415152704644016648854903873}\cdot t^{25}+\frac{1014606231423454269509566252562459553618110496273380653659903000}{7415152704644016648854903873}\cdot t^{23}-\frac{203601257036508811181048510459969191972683789912214056431659500}{322397943680174636906734951}\cdot t^{21}+\frac{737784117794120474352467421592075515386916409449357609578088750}{322397943680174636906734951}\cdot t^{19}-\frac{2064232006794952016469249466129428640028999622463207992397711125}{322397943680174636906734951}\cdot t^{17}+\frac{4365178114891828375976909398129475327882323198305898034429827125}{322397943680174636906734951}\cdot t^{15}-\frac{13573226541764359512112877067644374622643025796184740306915821875}{644795887360349273813469902}\cdot t^{13}+\frac{14955957100230567436520307496580240256684107881931787413640763125}{644795887360349273813469902}\cdot t^{11}-\frac{22211906932349895616595030350494398490633106080930340186936865625}{1289591774720698547626939804}\cdot t^9+\frac{82690123261719371557722400654468672889829855720797022720678384375}{10316734197765588381015518432}\cdot t^7-\frac{43059770877605033865122550893866932647923414272348478771780115625}{20633468395531176762031036864}\cdot t^5+\frac{10260314917027782078966752663381082515573578632233123841373265625}{41266936791062353524062073728}\cdot t^3-\frac{704503478680034222476782987315170565972480441964681437177046875}{82533873582124707048124147456}\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.