Rule: Q[1, 62]

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.

• $P_1$:
  $2\cdot t$
• $P_2$:
  $2\cdot t^{63}-1953\cdot t^{61}+\frac{1786995}{2}\cdot t^{59}-\frac{1019182815}{4}\cdot t^{57}+\frac{406653943185}{8}\cdot t^{55}-\frac{120776221125945}{16}\cdot t^{53}+\frac{27738272118592035}{32}\cdot t^{51}-\frac{5052328135886406375}{64}\cdot t^{49}+\frac{742692235975301737125}{128}\cdot t^{47}-\frac{89205589676589019759125}{256}\cdot t^{45}+\frac{8831353377982312956153375}{512}\cdot t^{43}-\frac{724973827301638963582408875}{1024}\cdot t^{41}+\frac{49539878198945329178131273125}{2048}\cdot t^{39}-\frac{2823773057339883763153482568125}{4096}\cdot t^{37}+\frac{134330918299168756161444242169375}{8192}\cdot t^{35}-\frac{5328459759200360661070621606051875}{16384}\cdot t^{33}+\frac{175839172053611901815330512999711875}{32768}\cdot t^{31}-\frac{4809718529701737314360511090874471875}{65536}\cdot t^{29}+\frac{108485873503272519423909305716390865625}{131072}\cdot t^{27}-\frac{2004133768402560753568008752971220728125}{262144}\cdot t^{25}+\frac{30062006526038411303520131294568310921875}{524288}\cdot t^{23}-\frac{362175602432748479037647296072656317296875}{1048576}\cdot t^{21}+\frac{3457130750494417299904815098875355756015625}{2097152}\cdot t^{19}-\frac{25703015579762841664509712256855905838203125}{4194304}\cdot t^{17}+\frac{145650421618656102765555036122183466416484375}{8388608}\cdot t^{15}-\frac{611731770798355631615331151713170558949234375}{16777216}\cdot t^{13}+\frac{1835195312395066894845993455139511676847703125}{33554432}\cdot t^{11}-\frac{3738360821545506637649245927136042304689765625}{67108864}\cdot t^9+\frac{4806463913415651391263316192032054391743984375}{134217728}\cdot t^7-\frac{3480542833852713076432056552850798007814609375}{268435456}\cdot t^5+\frac{1160180944617571025477352184283599335938203125}{536870912}\cdot t^3-\frac{112275575285571389562324404930670903477890625}{1073741824}\cdot t$

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.