#
# bessel.txt,  2 Apr 10

# As given in:
# J.F. Hart, Computer Approximations, New York, Willey 1968, p. 141
# and used in Numerical Recipes
# Also specified in Numerical recipes in C:1992

!fuzz 0.00000001

!msgpostfix Polynomial approximation for Bessel J0 function\n

!need all
 57568490574.0
-13362590354.0
   651619640.7
-   11214424.18
       77392.33017
-        184.9052456
 57568490411.0
  1029532985.0
     9494680.718
       59272.64853
         267.8532712
-          0.785398164

-0.1098628627e-2
 0.2734510407e-4
-0.2073370639e-5
 0.2093887211e-6

-0.1562499995e-1
 0.1430488765e-3
-0.6911147651e-5
 0.7621095161e-6
 0.934945152e-7

 0.636619772

# Also specified in Numerical recipes in C:1992
!msgpostfix Polynomial approximation for Bessel J1 function\n

!need all

 72362614232.0
- 7895059235.0
   242396853.1
-    2972611.439
       15704.48260
-         30.16036606

 144725228442.0
   2300535178.0
     18583304.74
        99447.43394
          376.9991397

 2.356194491

 0.183105e-2
-0.3516396496e-4
 0.2457520174e-5
-0.240337019e-6

 0.04687499995
-0.2002690873e-3
 0.8449199096e-5
-0.88228987e-6
 0.105787412e-6

 0.636619772


!msgpostfix Bessel function Y0 for positive x, Numerical recipes in C:1992\n

!need all
 8.0
- 2957821389.0
  7062834065.0
-  512359803.6
    10879881.29
-      86327.92757
         228.4622733
 40076544269.0
   745249964.8
     7189466.438
       47447.26470
         226.1030244
           0.636619772

-0.785398164
-0.1098628627e-2
 0.2734510407e-4
-0.2073370639e-5
 0.2093887211e-6
-0.1562499995e-1
 0.1430488765e-3
-0.6911147651e-5
 0.7621095161e-6
-0.934945152e-7
 0.636619772


!msgpostfix Bessel function Y1 for positive x, Numerical recipes in C:1992\n

!need all
 8.0
-0.4900604943e13
 0.1275274390e13
-0.5153438139e11
 0.7349264551e9
-0.4237922726e7
 0.8511937935e4
 0.2499580570e14
 0.4244419664e12
 0.3733650367e10
 0.2245904002e8
 0.1020426050e6
 0.3549632885e3
 0.636619772

 2.356194491
 0.183105e-2
-0.3516396496e-4
 0.2457520174e-5
-0.240337019e-6
 0.04687499995
-0.2002690873e-3
 0.8449199096e-5
-0.88228987e-6
 0.105787412e-6
 0.636619772


!msgpostfix modified Bessel function I0 for real x, Numerical recipes in C:1992\n

!need all
 3.75

 3.5156229
 3.0899424
 1.2067492
 0.2659732
 0.360768e-1
 0.45813e-2

 0.39894228
 0.1328592e-1
 0.225319e-2
-0.157565e-2
 0.916281e-2
-0.2057706e-1
 0.2635537e-1
-0.1647633e-1
 0.392377e-2

!msgpostfix modified Bessel function I0 for positive x, Numerical recipes in C:1992\n

!need all
 2.0
 4.0
-0.57721566
 0.42278420
 0.23069756
 0.3488590e-1
 0.262698e-2
 0.10750e-3
 0.74e-5

 1.25331414
-0.7832358e-1
 0.2189568e-1
-0.1062446e-1
 0.587872e-2
-0.251540e-2
 0.53208e-3


!msgpostfix modified Bessel function I1 for real x, Numerical recipes in C:1992\n

!need all
 3.75
 0.5
 0.87890594
 0.51498869
 0.15084934
 0.2658733e-1
 0.301532e-2
 0.32411e-3

 0.2282967e-1
-0.2895312e-1
 0.1787654e-1
-0.420059e-2
 0.39894228
-0.3988024e-1
-0.362018e-2
0.163801e-2
-0.1031555e-1


!msgpostfix modified Bessel function K1 for positive x, Numerical recipes in C:1992\n

!need all
 2.0
 4.0
 0.15443144
-0.67278579
-0.18156897
-0.1919402e-1
-0.110404e-2
-0.4686e-4

 1.25331414
 0.23498619
-0.3655620e-1
 0.1504268e-1
-0.780353e-2
 0.325614e-2
-0.68245e-3

# The Cephes Math Library tables are very long and not listed here..
# J0
# The domain is divided into two major intervals [0, 2] and
# (2, infinity). In the first interval the rational approximation
# is J0(x) = 1 - x^2 / 4 + x^4 R(x^2)
# The second interval is further partitioned into eight equal segments
# of 1/x.
#
# J0(x) = sqrt(2/(pi x)) (P0(x) cos(X) - Q0(x) sin(X)),
# X = x - pi/4,
#
# and the auxiliary functions are given by
#
# J0(x)cos(X) + Y0(x)sin(X) = sqrt( 2/(pi x)) P0(x),
# P0(x) = 1 + 1/x^2 R(1/x^2)
#
# Y0(x)cos(X) - J0(x)sin(X) = sqrt( 2/(pi x)) Q0(x),
# Q0(x) = 1/x (-.125 + 1/x^2 R(1/x^2))
#
# J1
# The domain is divided into two major intervals [0, 2] and
# (2, infinity). In the first interval the rational approximation is
# J1(x) = .5x + x x^2 R(x^2)
# 
# The second interval is further partitioned into eight equal segments
# of 1/x.
# J1(x) = sqrt(2/(pi x)) (P1(x) cos(X) - Q1(x) sin(X)),
# X = x - 3 pi / 4,
# 
# and the auxiliary functions are given by
# 
# J1(x)cos(X) + Y1(x)sin(X) = sqrt( 2/(pi x)) P1(x),
# P1(x) = 1 + 1/x^2 R(1/x^2)
# 
# Y1(x)cos(X) - J1(x)sin(X) = sqrt( 2/(pi x)) Q1(x),
# Q1(x) = 1/x (.375 + 1/x^2 R(1/x^2)).

