Graphics Programs Reference
In-Depth Information
=
The nodes are placed symmetricallyabout
x
0, each symmetric pair having the
same weight.
±
x
i
A
i
±
x
i
A
i
n
=
2
n
=
5
0
.
707107
0
.
886 227
0
.
000 000
0
.
945308
n
=
3
0
.
958 572
0
.
393 619
0
.
000 000
1
.
181 636
2
.
020 183
(
−
1) 0
.
199 532
.
.
=
1
224745
0
295 409
n
6
n
=
4
0
.
436 077
0
.
724 629
0
.
524 648
0
.
804 914
1
.
335 849
0
.
157 067
1
.
650 680
(
−
1)0
.
813 128
2
.
350 605
(
−
2)0
.
453 001
Table 6.5.
Multiply numbers by 10
k
, where
k
is giveninparentheses
√
π
n
!
2
2
(2
n
)!
f
(2
n
)
(
c
),
E
=
0
<
c
<
∞
(6.37)
Gauss quadrature with logarithmic singularity
1
n
f
(
x
)ln(
x
)
dx
≈
−
A
i
f
(
x
i
)
(6.38)
0
i
=
1
x
i
A
i
x
i
A
i
n
=
2
n
=
5
0
.
112 009
0
.
718 539
(
−
1)0
.
291 345
0
.
297 893
0
.
602 277
0
.
281 461
0
.
173 977
0
.
349 776
n
=
3
0
.
411 703
0
.
234488
(
−
1)0
.
638 907
0
.
513 405
0
.
677314
(
−
1)0
.
989 305
0
.
368 997
0
.
391 980
0
.
894 771
(
−
1)0
.
189 116
0
.
766 880
(
−
1)0
.
946154
n
=
6
n
=
4
(
−
1)0
.
216 344
0
.
238 764
−
.
.
.
.
(
1)0
414485
0
383 464
0
129 583
0
308 287
0
.
245 275
0
.
386 875
0
.
314020
0
.
245 317
0
.
556 165
0
.
190435
0
.
538 657
0
.
142 009
0
.
848 982
(
−
1)0
.
392 255
0
.
756 916
(
−
1)0
.
554 546
0
.
922 669
(
−
1)0
.
101690
Table 6.6.
Multiply numbers by 10
k
, where
k
is giveninparentheses
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