Geology Reference
In-Depth Information
Tabl e B. 1
Sample values of Legendre functions of the first kind calculated with
the programme LEGENDRE.FOR.
P
1
(
z
)
P
2
(
z
)
P
2
(
z
)
P
2
(
z
)
P
3
(
z
)
P
3
(
z
)
P
3
(
z
)
P
3
(
z
)
z
1.0
0.0000
1.0000
0.0000
0.0000
1.0000
0.0000
0.0000
0.0000
0.9
−
0.4359
0.7150
−
1.1769
0.5700
0.4725
−
1.9942
2.5650
−
1.2423
0.8
−
0.6000
0.4600
−
1.4400
1.0800
0.0800
−
1.9800
4.3200
−
3.2400
0.7
−
0.7141
0.2350
−
1.4997
1.5300
−
0.1925
−
1.5533
5.3550
−
5.4632
0.6
−
0.8000
0.0400
−
1.4400
1.9200
−
0.3600
−
0.9600
5.7600
−
7.6800
0.5
−
0.8660
−
0.1250
−
1.2990
2.2500
−
0.4375
−
0.3248
5.6250
−
9.7428
0.4
−
0.9165
−
0.2600
−
1.0998
2.5200
−
0.4400
0.2750
5.0400
−
11.5481
0.3
−
0.9539
−
0.3650
−
0.8585
2.7300
−
0.3825
0.7870
4.0950
−
13.0213
0.2
−
0.9798
−
0.4400
−
0.5879
2.8800
−
0.2800
1.1758
2.8800
−
14.1091
0.1
−
0.9950
−
0.4850
−
0.2985
2.9700
−
0.1475
1.4179
1.4850
−
14.7756
0.0
−
1.0000
−
0.5000
0.0000
3.0000
0.0000
1.5000
0.0000
−
15.0000
P3=((2.D0*AI-1.D0)*Z*P2-(AI+AM-1.D0)*P1)/(AI-AM)
P1=P2
P2=P3
16
CONTINUE
PMN=P3
GO TO 11
14
PMN=PMM
GO TO 11
15
PMN=PMMP1
11
CONTINUE
RETURN
END
Sample values of
P
n
(
z
) as output of these codes are given in Table B.1.
The first few Legendre functions in explicit form, beginning with the Legendre
polynomials, are as follows:
2
3
z
2
1
,
2
5
z
3
3
z
,
1
1
P
0
(
z
)
=
1,
P
2
(
z
)
=
−
P
3
(
z
)
=
−
P
2
(
z
)
=−
3
1
−
z
2
1/2
z
,
P
3
(
z
)
=−
2
1
−
z
2
1/2
5
z
2
−
1
,
3
P
1
(
z
)
=
z
,
3
1
−
z
2
,
15
1
−
z
2
z
,
P
1
(
z
)
−
z
)
1/2
,
P
2
(
z
)
P
3
(
z
)
=−
(1
=
=
15
1
z
2
3/2
P
3
(
z
)
=−
−
.
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