1Test of Y(X,ALPHA) vs Multiplication Theorem


   1986 Random arguments were tested from the interval ( 0.00, 2.00)


 Y(X,ALPHA) was larger   697 times,
                agreed   341 times, and
           was smaller   948 times.


 NOTE: first  14 arguments in test interval skipped
       because multiplication theorem did not converge


 There are  53 base   2 significant digits in a floating-point number


 The maximum relative error of     0.3190E-14 =    2 ** -48.16
    occurred for X = 0.192771E+01 and NU = 0.537715E+00
    with Y(X,ALPHA) =  0.173989E+00
 The estimated loss of base   2 significant digits is   4.84


 The root mean square relative error was     0.4108E-15 =    2 ** -51.11
 The estimated loss of base   2 significant digits is   1.89


1Test of Y(X,ALPHA) vs Taylor series


   2000 Random arguments were tested from the interval ( 2.00,10.00)


 Y(X,ALPHA) was larger   780 times,
                agreed   493 times, and
           was smaller   727 times.


 There are  53 base   2 significant digits in a floating-point number


 The maximum relative error of     0.5263E-14 =    2 ** -47.43
    occurred for X = 0.814265E+01 and NU = 0.572120E+00
    with Y(X,ALPHA) =  0.501005E-01
 The estimated loss of base   2 significant digits is   5.57


 The root mean square relative error was     0.3647E-15 =    2 ** -51.28
 The estimated loss of base   2 significant digits is   1.72


1Test of Y(X,ALPHA) vs Taylor series


   2000 Random arguments were tested from the interval (10.00,20.00)


 Y(X,ALPHA) was larger   696 times,
                agreed   569 times, and
           was smaller   735 times.


 There are  53 base   2 significant digits in a floating-point number


 The maximum relative error of     0.1161E-14 =    2 ** -49.61
    occurred for X = 0.160060E+02 and NU = 0.884626E+00
    with Y(X,ALPHA) =  0.191232E+00
 The estimated loss of base   2 significant digits is   3.39


 The root mean square relative error was     0.2332E-15 =    2 ** -51.93
 The estimated loss of base   2 significant digits is   1.07


1Test of Y(X,ALPHA) vs Taylor series


   2000 Random arguments were tested from the interval (30.00,40.00)


 Y(X,ALPHA) was larger   611 times,
                agreed   727 times, and
           was smaller   662 times.


 There are  53 base   2 significant digits in a floating-point number


 The maximum relative error of     0.2927E-14 =    2 ** -48.28
    occurred for X = 0.354124E+02 and NU = 0.272781E+00
    with Y(X,ALPHA) =  0.474170E-01
 The estimated loss of base   2 significant digits is   4.72


 The root mean square relative error was     0.1963E-15 =    2 ** -52.18
 The estimated loss of base   2 significant digits is   0.82


1Check of Error Returns


 The following summarizes calls with indicated parameters

 NCALC different from MB indicates some form of error

 See documentation for RYBESL for details

       ARG            ALPHA      MB      B(1)      NCALC


  0.1000000E+01  0.1500000E+01    5  0.0000000E+00   -1


  0.1000000E+01  0.5000000E+00    2 -0.4310989E+00    2


  0.2225074-307  0.0000000E+00    2  0.0000000E+00   -1


  0.6675222-307  0.0000000E+00    2 -0.4503536E+03    2


  0.6675222-307  0.1000000E+01    2 -0.9537058+307    1


 Tests near the largest acceptable argument for RYBESL

 RYBESL will be called with the arguments 0.335544E+08 0.500000E+00
 NCALC returned the value    2
 and RYBESL returned U(1) =  0.296749E-04

 RYBESL will be called with the arguments 0.536871E+09 0.500000E+00
 This should trigger an error message.
 NCALC returned the value   -1
 and RYBESL returned U(1) =  0.000000E+00

 This concludes the tests.
