Laguerre Polynomials

Download

This page provides an overview of the rules of Laguerre type. All rules listed below can be downloaded packed into a single file here:

• csv files with nodes and weights
• raw text files as output by the 'kes' software

The csv files contain row by row in this order:

• real part of the values of the nodes
• imaginary part of the values of the nodes (should be small)
• real part of the values of the weights
• imaginary part of the values of the weights (should be small)
• real part of the maximal error of the nodes (should be tiny)
• imaginary part of the maximal error of the nodes (should be tiny)
• real part of the maximal error of the weights (should be tiny)
• imaginary part of the maximal error of the weights (should be tiny)

Detailed Listing

Note: Rules printed in red have negative weights.

Base Polynomial Order 1

Maximal search order: 100
Maximal recursion depth: 6

• Q[1]
• Q[1, 3]
• Q[1, 3, 5]
• Q[1, 3, 5, 8]
• Q[1, 3, 5, 8, 32]
• Q[1, 3, 5, 8, 33]
• Q[1, 3, 5, 9]
• Q[1, 3, 5, 10]
• Q[1, 3, 5, 11]
• Q[1, 3, 5, 12]
• Q[1, 3, 5, 12, 24]
• Q[1, 3, 5, 12, 25]
• Q[1, 3, 5, 12, 26]
• Q[1, 3, 5, 23]
• Q[1, 3, 5, 24]
• Q[1, 3, 5, 25]
• Q[1, 3, 5, 28]
• Q[1, 3, 5, 29]
• Q[1, 3, 5, 45]
• Q[1, 3, 5, 46]
• Q[1, 3, 5, 47]
• Q[1, 3, 5, 69]
• Q[1, 3, 5, 70]
• Q[1, 3, 5, 80]
• Q[1, 3, 6]
• Q[1, 3, 6, 43]
• Q[1, 3, 6, 91]
• Q[1, 3, 6, 92]
• Q[1, 3, 6, 93]
• Q[1, 3, 7]
• Q[1, 3, 7, 90]
• Q[1, 3, 7, 91]
• Q[1, 3, 8]
• Q[1, 3, 8, 89]
• Q[1, 3, 8, 90]
• Q[1, 3, 10]
• Q[1, 3, 11]
• Q[1, 3, 17]
• Q[1, 3, 18]
• Q[1, 3, 19]
• Q[1, 3, 20]
• Q[1, 3, 21]
• Q[1, 3, 22]
• Q[1, 3, 51]
• Q[1, 3, 52]
• Q[1, 3, 53]
• Q[1, 3, 54]
• Q[1, 3, 59]
• Q[1, 3, 60]
• Q[1, 3, 61]
• Q[1, 3, 62]
• Q[1, 3, 63]
• Q[1, 3, 78]
• Q[1, 3, 79]
• Q[1, 3, 80]
• Q[1, 3, 81]
• Q[1, 3, 82]
• Q[1, 3, 83]
• Q[1, 3, 88]
• Q[1, 3, 89]
• Q[1, 3, 90]
• Q[1, 3, 91]
• Q[1, 3, 92]
• Q[1, 3, 93]
• Q[1, 4]
• Q[1, 4, 10]
• Q[1, 4, 21]
• Q[1, 4, 22]
• Q[1, 4, 26]
• Q[1, 4, 31]
• Q[1, 4, 32]
• Q[1, 4, 33]
• Q[1, 4, 34]
• Q[1, 4, 72]
• Q[1, 4, 89]
• Q[1, 4, 90]
• Q[1, 4, 91]
• Q[1, 4, 92]
• Q[1, 4, 93]
• Q[1, 4, 94]
• Q[1, 5]
• Q[1, 5, 11]
• Q[1, 5, 11, 68]
• Q[1, 5, 14]
• Q[1, 5, 15]
• Q[1, 5, 21]
• Q[1, 5, 34]
• Q[1, 5, 35]
• Q[1, 5, 36]
• Q[1, 5, 39]
• Q[1, 5, 45]
• Q[1, 5, 77]
• Q[1, 5, 78]
• Q[1, 5, 79]
• Q[1, 5, 80]
• Q[1, 5, 81]
• Q[1, 6]
• Q[1, 6, 12]
• Q[1, 6, 13]
• Q[1, 6, 15]
• Q[1, 6, 52]
• Q[1, 6, 82]
• Q[1, 6, 83]
• Q[1, 6, 84]
• Q[1, 6, 85]
• Q[1, 7]
• Q[1, 7, 12]
• Q[1, 7, 47]
• Q[1, 7, 83]
• Q[1, 7, 84]
• Q[1, 7, 85]
• Q[1, 12]
• Q[1, 12, 20]
• Q[1, 12, 21]
• Q[1, 13]
• Q[1, 14]
• Q[1, 15]
• Q[1, 16]
• Q[1, 17]
• Q[1, 18]
• Q[1, 25]
• Q[1, 26]
• Q[1, 27]
• Q[1, 28]
• Q[1, 29]
• Q[1, 30]
• Q[1, 31]
• Q[1, 32]
• Q[1, 33]
• Q[1, 34]
• Q[1, 44]
• Q[1, 45]
• Q[1, 46]
• Q[1, 47]
• Q[1, 48]
• Q[1, 49]
• Q[1, 50]
• Q[1, 51]
• Q[1, 52]
• Q[1, 53]
• Q[1, 54]
• Q[1, 55]
• Q[1, 67]
• Q[1, 68]
• Q[1, 69]
• Q[1, 70]
• Q[1, 71]
• Q[1, 72]
• Q[1, 73]
• Q[1, 74]
• Q[1, 75]
• Q[1, 76]
• Q[1, 77]
• Q[1, 78]
• Q[1, 79]
• Q[1, 80]
• Q[1, 81]
• Q[1, 96]
• Q[1, 97]
• Q[1, 98]
• Q[1, 99]
• Q[1, 100]

Base Polynomial Order 2

Maximal search order: 100
Maximal recursion depth: 6

• Q[2]
• Q[2, 4]
• Q[2, 4, 7]
• Q[2, 4, 7, 29]
• Q[2, 4, 8]
• Q[2, 4, 8, 86]
• Q[2, 4, 9]
• Q[2, 4, 9, 86]
• Q[2, 4, 10]
• Q[2, 4, 13]
• Q[2, 4, 21]
• Q[2, 4, 22]
• Q[2, 4, 23]
• Q[2, 4, 30]
• Q[2, 4, 41]
• Q[2, 4, 42]
• Q[2, 4, 43]
• Q[2, 4, 44]
• Q[2, 4, 45]
• Q[2, 4, 47]
• Q[2, 4, 53]
• Q[2, 4, 68]
• Q[2, 4, 69]
• Q[2, 4, 70]
• Q[2, 4, 71]
• Q[2, 4, 72]
• Q[2, 4, 73]
• Q[2, 4, 74]
• Q[2, 4, 96]
• Q[2, 4, 97]
• Q[2, 5]
• Q[2, 5, 29]
• Q[2, 5, 30]
• Q[2, 5, 38]
• Q[2, 5, 39]
• Q[2, 5, 48]
• Q[2, 6]
• Q[2, 6, 50]
• Q[2, 6, 51]
• Q[2, 6, 54]
• Q[2, 6, 79]
• Q[2, 6, 80]
• Q[2, 7]
• Q[2, 7, 49]
• Q[2, 7, 77]
• Q[2, 9]
• Q[2, 9, 48]
• Q[2, 10]
• Q[2, 10, 58]
• Q[2, 11]
• Q[2, 15]
• Q[2, 16]
• Q[2, 23]
• Q[2, 24]
• Q[2, 25]
• Q[2, 26]
• Q[2, 27]
• Q[2, 28]
• Q[2, 29]
• Q[2, 30]
• Q[2, 42]
• Q[2, 43]
• Q[2, 44]
• Q[2, 45]
• Q[2, 46]
• Q[2, 47]
• Q[2, 48]
• Q[2, 49]
• Q[2, 54]
• Q[2, 55]
• Q[2, 56]
• Q[2, 57]
• Q[2, 58]
• Q[2, 68]
• Q[2, 69]
• Q[2, 70]
• Q[2, 71]
• Q[2, 72]
• Q[2, 73]
• Q[2, 74]
• Q[2, 75]
• Q[2, 83]
• Q[2, 84]
• Q[2, 85]
• Q[2, 86]
• Q[2, 87]
• Q[2, 88]
• Q[2, 89]
• Q[2, 90]
• Q[2, 91]
• Q[2, 92]
• Q[2, 93]
• Q[2, 94]
• Q[2, 99]

Base Polynomial Order 3

Maximal search order: 100
Maximal recursion depth: 6

• Q[3]
• Q[3, 6]
• Q[3, 6, 41]
• Q[3, 6, 42]
• Q[3, 6, 43]
• Q[3, 6, 44]
• Q[3, 6, 50]
• Q[3, 7]
• Q[3, 7, 57]
• Q[3, 7, 58]
• Q[3, 7, 94]
• Q[3, 8]
• Q[3, 10]
• Q[3, 15]
• Q[3, 16]
• Q[3, 20]
• Q[3, 28]
• Q[3, 33]
• Q[3, 34]
• Q[3, 35]
• Q[3, 36]
• Q[3, 37]
• Q[3, 58]
• Q[3, 59]
• Q[3, 60]
• Q[3, 68]
• Q[3, 69]
• Q[3, 70]
• Q[3, 71]
• Q[3, 72]
• Q[3, 73]
• Q[3, 74]
• Q[3, 75]
• Q[3, 76]

Base Polynomial Order 4

Maximal search order: 100
Maximal recursion depth: 6

• Q[4]
• Q[4, 8]
• Q[4, 9]
• Q[4, 11]
• Q[4, 19]
• Q[4, 20]
• Q[4, 29]
• Q[4, 30]
• Q[4, 31]
• Q[4, 42]
• Q[4, 49]
• Q[4, 50]
• Q[4, 51]
• Q[4, 82]
• Q[4, 83]
• Q[4, 84]
• Q[4, 85]
• Q[4, 86]
• Q[4, 87]
• Q[4, 88]
• Q[4, 93]
• Q[4, 94]
• Q[4, 95]
• Q[4, 96]
• Q[4, 97]

Base Polynomial Order 5

Maximal search order: 100
Maximal recursion depth: 6

• Q[5]
• Q[5, 9]
• Q[5, 9, 39]
• Q[5, 9, 40]
• Q[5, 10]
• Q[5, 12]
• Q[5, 25]
• Q[5, 44]
• Q[5, 57]
• Q[5, 58]
• Q[5, 59]
• Q[5, 60]
• Q[5, 61]
• Q[5, 62]
• Q[5, 63]
• Q[5, 72]
• Q[5, 99]
• Q[5, 100]

Base Polynomial Order 6

Maximal search order: 100
Maximal recursion depth: 6

• Q[6]
• Q[6, 11]
• Q[6, 12]
• Q[6, 13]
• Q[6, 14]
• Q[6, 47]
• Q[6, 66]
• Q[6, 67]
• Q[6, 68]
• Q[6, 69]
• Q[6, 73]
• Q[6, 74]
• Q[6, 75]
• Q[6, 76]
• Q[6, 78]

Base Polynomial Order 7

Maximal search order: 100
Maximal recursion depth: 6

• Q[7]
• Q[7, 12]
• Q[7, 13]
• Q[7, 15]
• Q[7, 80]
• Q[7, 81]
• Q[7, 82]
• Q[7, 83]
• Q[7, 86]
• Q[7, 87]

Base Polynomial Order 8

Maximal search order: 100
Maximal recursion depth: 6

• Q[8]
• Q[8, 13]
• Q[8, 15]
• Q[8, 15, 26]
• Q[8, 16]
• Q[8, 40]
• Q[8, 54]
• Q[8, 88]
• Q[8, 89]
• Q[8, 90]

Base Polynomial Order 9

Maximal search order: 100
Maximal recursion depth: 6

• Q[9]
• Q[9, 17]

Base Polynomial Order 10

Maximal search order: 100
Maximal recursion depth: 6

• Q[10]
• Q[10, 18]

Base Polynomial Order 11

Maximal search order: 100
Maximal recursion depth: 6

• Q[11]
• Q[11, 20]

Base Polynomial Order 12

Maximal search order: 100
Maximal recursion depth: 6

• Q[12]
• Q[12, 21]

Base Polynomial Order 13

Maximal search order: 100
Maximal recursion depth: 6

• Q[13]

Base Polynomial Order 14

Maximal search order: 100
Maximal recursion depth: 6

• Q[14]

Base Polynomial Order 15

Maximal search order: 100
Maximal recursion depth: 6

• Q[15]

Base Polynomial Order 16

Maximal search order: 100
Maximal recursion depth: 6

• Q[16]

Base Polynomial Order 17

Maximal search order: 100
Maximal recursion depth: 6

• Q[17]

Base Polynomial Order 18

Maximal search order: 100
Maximal recursion depth: 6

• Q[18]

Base Polynomial Order 19

Maximal search order: 100
Maximal recursion depth: 6

• Q[19]

Base Polynomial Order 20

Maximal search order: 100
Maximal recursion depth: 6

• Q[20]

Base Polynomial Order 21

Maximal search order: 100
Maximal recursion depth: 6

• Q[21]

Base Polynomial Order 22

Maximal search order: 100
Maximal recursion depth: 6

• Q[22]

Base Polynomial Order 23

Maximal search order: 100
Maximal recursion depth: 6

• Q[23]

Base Polynomial Order 24

Maximal search order: 100
Maximal recursion depth: 6

• Q[24]

Base Polynomial Order 25

Maximal search order: 100
Maximal recursion depth: 6

• Q[25]

Base Polynomial Order 26

Maximal search order: 100
Maximal recursion depth: 6

• Q[26]

Base Polynomial Order 27

Maximal search order: 100
Maximal recursion depth: 6

• Q[27]

Base Polynomial Order 28

Maximal search order: 100
Maximal recursion depth: 6

• Q[28]

Base Polynomial Order 29

Maximal search order: 100
Maximal recursion depth: 6

• Q[29]

Base Polynomial Order 30

Maximal search order: 100
Maximal recursion depth: 6

• Q[30]

Base Polynomial Order 31

Maximal search order: 100
Maximal recursion depth: 6

• Q[31]

Base Polynomial Order 32

Maximal search order: 100
Maximal recursion depth: 6

• Q[32]

Base Polynomial Order 33

Maximal search order: 100
Maximal recursion depth: 6

• Q[33]

Base Polynomial Order 34

Maximal search order: 100
Maximal recursion depth: 6

• Q[34]

Base Polynomial Order 35

Maximal search order: 100
Maximal recursion depth: 6

• Q[35]

Base Polynomial Order 36

Maximal search order: 100
Maximal recursion depth: 6

• Q[36]

Base Polynomial Order 37

Maximal search order: 100
Maximal recursion depth: 6

• Q[37]

Base Polynomial Order 38

Maximal search order: 100
Maximal recursion depth: 6

• Q[38]

Base Polynomial Order 39

Maximal search order: 100
Maximal recursion depth: 6

• Q[39]

Base Polynomial Order 40

Maximal search order: 100
Maximal recursion depth: 6

• Q[40]

Base Polynomial Order 41

Maximal search order: 100
Maximal recursion depth: 6

• Q[41]

Base Polynomial Order 42

Maximal search order: 100
Maximal recursion depth: 6

• Q[42]

Base Polynomial Order 43

Maximal search order: 100
Maximal recursion depth: 6

• Q[43]

Base Polynomial Order 44

Maximal search order: 100
Maximal recursion depth: 6

• Q[44]

Base Polynomial Order 45

Maximal search order: 100
Maximal recursion depth: 6

• Q[45]

Base Polynomial Order 46

Maximal search order: 100
Maximal recursion depth: 6

• Q[46]

Base Polynomial Order 47

Maximal search order: 100
Maximal recursion depth: 6

• Q[47]

Base Polynomial Order 48

Maximal search order: 100
Maximal recursion depth: 6

• Q[48]

Base Polynomial Order 49

Maximal search order: 100
Maximal recursion depth: 6

• Q[49]

Base Polynomial Order 50

Maximal search order: 100
Maximal recursion depth: 6

• Q[50]