Rule: Q[1, 88]

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^{89}-3916\cdot t^{87}+3662439\cdot t^{85}-2179151205\cdot t^{83}+\frac{7415651550615}{8}\cdot t^{81}-\frac{600667775599815}{2}\cdot t^{79}+\frac{616885805541010005}{8}\cdot t^{77}-\frac{128929133358071091045}{8}\cdot t^{75}+\frac{357778345068647277649875}{128}\cdot t^{73}-\frac{26117819190011251268440875}{64}\cdot t^{71}+\frac{12980556137435591880415114875}{256}\cdot t^{69}-\frac{1384199304473813570520629977125}{256}\cdot t^{67}+\frac{1020154887397200601473704293141125}{2048}\cdot t^{65}-\frac{5100774436986003007368521465705625}{128}\cdot t^{63}+\frac{1423116067919094839055817488931869375}{512}\cdot t^{61}-\frac{86810080143064785182404866824844031875}{512}\cdot t^{59}+\frac{148532047124783847447094727137308138538125}{16384}\cdot t^{57}-\frac{3486134517811103243022988007516820428041875}{8192}\cdot t^{55}+\frac{575212195438832035098793021240275370626909375}{32768}\cdot t^{53}-\frac{20859010666176593272793073243923670019049503125}{32768}\cdot t^{51}+\frac{5319047719875031284562233677200535854857623296875}{262144}\cdot t^{49}-\frac{37233334039125218991935635740403750984003363078125}{65536}\cdot t^{47}+\frac{3659021281481305611843856566852404983064330498859375}{262144}\cdot t^{45}-\frac{78748501492749838167943869590953933331167112910234375}{262144}\cdot t^{43}+\frac{23703298949317701288551104746877133932681300985980546875}{4194304}\cdot t^{41}-\frac{194367051384405150566119058924392498247986668085040484375}{2097152}\cdot t^{39}+\frac{11078921928911093582268786358690372400135240080847307609375}{8388608}\cdot t^{37}-\frac{136640037123236820847981698423847926268334627663783460515625}{8388608}\cdot t^{35}+\frac{11614403155475129772078444366027073732808443351421594143828125}{67108864}\cdot t^{33}-\frac{13216389797609630430296160830306670109747538986100434715390625}{8388608}\cdot t^{31}+\frac{409708083725898543339180985739506773402173708569113476177109375}{33554432}\cdot t^{29}-\frac{2682927128914754977350120648552254032278750414178388247224296875}{33554432}\cdot t^{27}+\frac{941707422249078997049892347641841165329841395376614274775728203125}{2147483648}\cdot t^{25}-\frac{2140244141475179538749755335549639012113275898583214260853927734375}{1073741824}\cdot t^{23}+\frac{31851868693718848429628711758474039415568164843620776940943748046875}{4294967296}\cdot t^{21}-\frac{95555606081156545288886135275422118246704494530862330822831244140625}{4294967296}\cdot t^{19}+\frac{1815556515541974360488836570233020246687385396086384285633793638671875}{34359738368}\cdot t^{17}-\frac{834174615249015246711087072809766059288798695499149536642553833984375}{8589934592}\cdot t^{15}+\frac{4609912347428768468666533823422391380280203317232142176182534345703125}{34359738368}\cdot t^{13}-\frac{4609912347428768468666533823422391380280203317232142176182534345703125}{34359738368}\cdot t^{11}+\frac{50709035821716453155331872057646305183082236489553563938007877802734375}{549755813888}\cdot t^9-\frac{11131251765742636058487484110215042601164393375755660376635875615234375}{274877906944}\cdot t^7+\frac{11131251765742636058487484110215042601164393375755660376635875615234375}{1099511627776}\cdot t^5-\frac{1294331600667748378893893501187795651298185276250658183329752978515625}{1099511627776}\cdot t^3+\frac{352999527454840466971061863960307904899505075341088595453568994140625}{8796093022208}\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.