Rule: Q[12, 25]

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.

• $P_1$:
  $4096\cdot t^{12}-135168\cdot t^{10}+1520640\cdot t^8-7096320\cdot t^6+13305600\cdot t^4-7983360\cdot t^2+665280$
• $P_2$:
  $4096\cdot t^{37}-\frac{4593423486910464}{4258858723}\cdot t^{35}+\frac{9153662054444835840}{72400598291}\cdot t^{33}-\frac{632913033519199825920}{72400598291}\cdot t^{31}+\frac{28834127094943251417600}{72400598291}\cdot t^{29}-\frac{6410448273676917850744320}{506804188037}\cdot t^{27}+\frac{1904072707915385965779127680}{6588454444481}\cdot t^{25}-\frac{31837945187368623155060736000}{6588454444481}\cdot t^{23}+\frac{56075211291939137285646384000}{941207777783}\cdot t^{21}-\frac{509712538961932573236078780000}{941207777783}\cdot t^{19}+\frac{3392448678087065091445106574000}{941207777783}\cdot t^{17}-\frac{959054438215667001284714286000}{55365163399}\cdot t^{15}+\frac{3255793892271702277374179688750}{55365163399}\cdot t^{13}-\frac{14181373232346765241319613750}{103874603}\cdot t^{11}+\frac{1761365357209300500836843259375}{8517717446}\cdot t^9-\frac{115892524887771078928195976250}{608408389}\cdot t^7+\frac{929037777119335903616440531875}{9734534224}\cdot t^5-\frac{103651561055887454387701996875}{4867267112}\cdot t^3+\frac{52070220494912921376023128125}{38938136896}\cdot t$

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.