📄 fncval.dat
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Values of Special Functions in format x,F(x) or x,y,F(x,y)
Dawson integral
4 Values
0.04 0.0399573606
0.16 0.1572970920
1.6 0.3999398943
10.0 0.0502538471
Ordinary Bessel Functions nu,x,jnu(x),ynu(x),jnup(x),ynup(x)
20 Values
2.0 1.0 1.149034849E-01 -1.650682607E+00 2.102436159E-01 2.520152392E+00
2.0 2.0 3.528340286E-01 -6.174081042E-01 2.238907791E-01 5.103756726E-01
2.0 5.0 4.656511628E-02 3.676628826E-01 -3.462051841E-01 7.979903490E-04
2.0 10.0 2.546303137E-01 -5.868082442E-03 -7.453316568E-03 2.501890407E-01
2.0 50.0 -5.971280079E-02 9.579316873E-02 -9.512331609E-02 -6.062739531E-02
5.0 1.0 2.497577302E-04 -2.604058666E+02 1.227850313E-03 1.268750910E+03
5.0 2.0 7.039629756E-03 -9.935989128E+00 1.639664542E-02 2.207402959E+01
5.0 5.0 2.611405461E-01 -4.536948225E-01 1.300918143E-01 2.615525351E-01
5.0 10.0 -2.340615282E-01 1.354030477E-01 -1.025719220E-01 -2.126510357E-01
5.0 50.0 -8.140024770E-02 -7.854841391E-02 7.898100205E-02 -8.020323269E-02
10.0 1.0 2.630615124E-10 -1.216180143E+08 2.618635056E-09 1.209399938E+09
10.0 2.0 2.515386283E-07 -1.291845422E+05 1.234650294E-06 6.313628817E+05
10.0 5.0 1.467802647E-03 -2.512911010E+01 2.584677845E-03 4.249433700E+01
10.0 10.0 2.074861066E-01 -3.598141522E-01 8.436957863E-02 1.605148864E-01
10.0 50.0 -1.138478491E-01 5.723897182E-03 -4.422891214E-03 -1.116145748E-01
20.0 1.0 3.873503009E-25 -4.113970315E+22 7.737778395E-24 8.217106466E+23
20.0 2.0 3.918972805E-19 -4.081651389E+16 3.900270468E-18 4.060105807E+17
20.0 5.0 2.770330052E-11 -5.933965297E+08 1.074693821E-10 2.294022549E+09
20.0 10.0 1.151336925E-05 -1.597483848E+03 2.011953903E-05 2.737803151E+03
20.0 50.0 -1.167043528E-01 1.644263395E-02 -1.368329398E-02 -1.071717186E-01
Modified Bessel Functions nu,x,inu(x),knu(x),inup(x),knup(x)
28 Values
2.0 0.2 5.016687514E-03 4.951242929E+01 5.033395889E-02 -4.999002654E+02
2.0 1.0 1.357476698E-01 1.624838899E+00 2.936637645E-01 -3.851585027E+00
2.0 2.0 6.889484477E-01 2.537597546E-01 9.016884069E-01 -3.936256364E-01
2.0 2.5 1.276466148E+00 1.214602063E-01 1.495543327E+00 -1.710589814E-01
2.0 3.0 2.245212441E+00 6.151045847E-02 2.456561923E+00 -8.116340344E-02
2.0 5.0 1.750561497E+01 5.308943712E-03 1.733339616E+01 -6.168190930E-03
2.0 10.0 2.281518968E+03 2.150981701E-05 2.214684510E+03 -2.295073686E-05
2.0 20.0 3.931278522E+07 6.329543612E-10 3.852369486E+07 -6.516012331E-10
3.0 1.0 2.216842492E-02 7.101262825E+00 6.924239499E-02 -2.292862737E+01
3.0 2.0 2.127399592E-01 6.473853909E-01 3.698385088E-01 -1.224837841E+00
3.0 5.0 1.033115017E+01 8.291768415E-03 1.130692487E+01 -1.028400476E-02
3.0 10.0 1.758380717E+03 2.725270026E-05 1.754004753E+03 -2.968562708E-05
3.0 50.0 2.677764139E+20 3.727936774E-23 2.655764792E+20 -3.771608045E-23
5.0 1.0 2.714631560E-04 3.609605896E+02 1.379804441E-03 -1.849035364E+03
5.0 2.0 9.825679323E-03 9.431049101E+00 2.616437167E-02 -2.577353868E+01
5.0 5.0 2.157974547E+00 3.270627371E-02 2.950260216E+00 -4.796533952E-02
5.0 10.0 7.771882864E+02 5.754184999E-05 8.378963946E+02 -6.663236215E-05
5.0 50.0 2.278548308E+20 4.367182254E-23 2.267244113E+20 -4.432002477E-23
10.0 1.0 2.752948040E-10 1.807132899E+08 2.765437823E-09 -1.817137940E+09
10.0 2.0 3.016963879E-07 1.624824040E+05 1.535703963E-06 -8.302224962E+05
10.0 5.0 4.580044419E-03 9.758562829E+00 1.015562998E-02 -2.202940355E+01
10.0 10.0 2.189170616E+01 1.614255300E-03 3.042758634E+01 -2.324264134E-03
10.0 50.0 1.071597159E+20 9.150988210E-23 1.082473779E+20 -9.419859989E-23
20.0 1.0 3.966835986E-25 6.294369360E+22 7.943111714E-24 -1.260529076E+24
20.0 2.0 4.310560576E-19 5.770856853E+16 4.331042808E-18 -5.801141519E+17
20.0 5.0 5.024239358E-11 4.827000521E+08 2.068719274E-10 -1.993195442E+09
20.0 10.0 1.250799736E-04 1.787442782E+02 2.784778118E-04 -4.015325804E+02
20.0 50.0 5.442008403E+18 1.706148380E-21 5.814242572E+18 -1.852264589E-21
Spherical Bessel Functions n,x,sjn(x),syn(x),sjnp(x),synp(x)
11 Values
0 0.1 9.9833417E-01 -9.9500417E+00 -3.3300012E-02 1.0049875E+02
0 1.0 8.4147098E-01 -5.4030231E-01 -3.0116868E-01 1.3817733E+00
0 5.0 -1.9178485E-01 -5.6732437E-02 9.5089408E-02 -1.8043837E-01
0 50.0 -5.2474971E-03 -1.9299321E-02 1.9404271E-02 -4.8615107E-03
1 0.1 3.3300012E-02 -1.0049875E+02 3.3233393E-01 2.0000250E+03
1 1.0 3.0116868E-01 -1.3817733E+00 2.3913363E-01 2.2232443E+00
1 5.0 -9.5089408E-02 1.8043837E-01 -1.5374909E-01 -1.2890778E-01
1 50.0 -1.9404271E-02 4.8615107E-03 -4.4713263E-03 -1.9493781E-02
20 1.0 7.5377957E-26 -3.2395922E+23 1.5058053E-24 6.7948312E+24
20 5.0 5.4277268E-12 -9.2679514E+08 2.1071414E-11 3.7715819E+09
20 50.0 -1.5785030E-02 1.3759531E-02 -1.2204181E-02 -1.4702296E-02
Airy Functions
8 Values
-3.5 -0.37553382 0.16893984 -0.34344343 -0.69311628
-2.0 0.22740743 -0.41230259 0.61825902 0.27879517
-1.0 0.53556088 0.10399739 -0.01016057 0.59237563
-0.01 0.35761619 0.61044364 -0.25880157 0.44831896
0.00 0.35502805 0.61492663 -0.25881940 0.44828836
0.01 0.35243992 0.61940962 -0.25880174 0.44831926
0.5 0.23169361 0.85427704 -0.22491053 0.54457256
1.00 0.13529242 1.20742359 -0.15914744 0.93243593
Elliptic Integral First Kind RF
3 Values
0.1 0.1 0.1 3.16227766
0.0 1.0 2.0 1.31102878
100.0 100.0 100.0 0.1
Elliptic Integral Second Kind RD
3 Values
0.1 0.1 0.1 31.6227766
0.0 2.0 1.0 1.79721036
100.0 100.0 100.0 0.001
Elliptic Integral Third Kind RJ
3 Values
0.1 0.1 0.1 0.1 31.6227766
2.0 3.0 4.0 5.0 0.142975797
100.0 100.0 100.0 100.0 0.001
Elliptic Integral Degenerate RC
5 Values
0.1 0.1 3.16227766
0.0 0.25 3.14159265
0.0625 0.125 3.14159265
2.25 2.0 0.69314718
100.0 100.0 0.1
Legendre Elliptic Integral First Kind
9 Values
5.0 2.0 0.08726660
5.0 30.0 0.08729413
5.0 88.0 0.08737730
30.0 2.0 0.52362636
30.0 30.0 0.52942863
30.0 88.0 0.54927042
90.0 2.0 1.57127495
90.0 30.0 1.68575035
90.0 88.0 4.74271727
Legendre Elliptic Integral Second Kind
9 Values
5.0 2.0 0.08726633
5.0 30.0 0.08723881
5.0 88.0 0.08715588
30.0 2.0 0.52357119
30.0 30.0 0.51788193
30.0 88.0 0.50003003
90.0 2.0 1.57031792
90.0 30.0 1.46746221
90.0 88.0 1.00258409
Legendre Elliptic Integral Third Kind
12 Values
15.0 0.4 30.0 0.264953
60.0 0.6 90.0 1.71951
90.0 0.0 30.0 1.68575
90.0 0.9 75.0 12.46407
15.0 1.0 15.0 0.268156
45.0 0.0625 30.0 0.813845
45.0 0.625 30.0 0.921130
45.0 1.25 30.0 1.132136
45.0 -0.25 30.0 0.769872
90.0 0.0625 30.0 1.743055
90.0 0.625 30.0 2.800989
90.0 -0.25 30.0 1.501762
Fresnel Integrals
6 Values
0.1 0.0005236 0.0999975
1.0 0.4382591 0.7798934
1.5 0.6975050 0.4452612
2.0 0.3434157 0.4882534
5.0 0.4991914 0.5636312
20.0 0.4840845 0.4999873
Exponential Integral En n,x,En(x)
13 Values
0 1.0 0.3678794
2 0.0 1.0000000
3 0.0 0.5000000
4 0.0 0.3333333
2 0.5 0.3266439
3 0.5 0.2216044
4 0.5 0.1652428
10 0.5 0.0634583
20 0.5 0.0310612
2 5.0 0.9964690E-03
20 5.0 0.2782746E-03
2 50.0 0.3711783E-23
20 50.0 0.2766423E-23
Cosine and Sine Integrals
17 Values
0.1 -1.727868E+00 9.994446E-02
0.2 -1.042206E+00 1.995561E-01
0.6 -2.227071E-02 5.881288E-01
0.7 1.005147E-01 6.812222E-01
1.8 4.568111E-01 1.505817E+00
1.9 4.419403E-01 1.557775E+00
2.0 4.229808E-01 1.605413E+00
2.1 4.005120E-01 1.648699E+00
2.2 3.750746E-01 1.687625E+00
3.3 2.467829E-02 1.848081E+00
6.3 -1.988822E-02 1.418174E+00
6.4 -4.181411E-03 1.419223E+00
6.5 1.110152E-02 1.421794E+00
6.6 2.582314E-02 1.425816E+00
10.0 -4.545644E-02 1.658348E+00
12.5 -1.140835E-02 1.492337E+00
15.0 4.627868E-02 1.618194E+00
Exponential Integral Ei
21 Values
0.1 -1.62281
0.2 -0.821761
0.3 -0.302669
0.4 0.104768
0.5 0.454220
0.6 0.769881
0.7 1.06491
0.8 1.34740
0.9 1.62281
2.2 5.73261
2.4 6.60067
3.5 13.9254
3.9 18.3157
5.0 40.1853
5.4 54.1935
12.5 23565.1
13.0 37197.7
13.5 58827.0
14.0 93193.0
14.5 147866.
15.0 234955.
Gamma Function
17 Values
1.0 1.000000
1.2 0.918169
1.4 0.887264
1.6 0.893515
1.8 0.931384
2.0 1.000000
0.2 4.590845
0.4 2.218160
0.6 1.489192
0.8 1.164230
-0.2 -5.821149
-0.4 -3.722981
-0.6 -3.696933
-0.8 -5.738555
10.0 3.6288000E05
20.0 1.2164510E17
30.0 8.8417620E30
N-factorial
18 Values
1 1
2 2
3 6
4 24
5 120
6 720
7 5040
8 40320
9 362880
10 3628800
11 39916800
12 479001600
13 6227020800
14 87178291200
15 1.3076755E12
20 2.4329042E18
25 1.5511222E25
30 2.6525281E32
Binomial Coefficients
20 Values
1 0 1
6 1 6
6 3 20
6 5 6
15 1 15
15 3 455
15 5 3003
15 7 6435
15 9 5005
15 11 1365
15 13 105
25 1 25
25 3 2300
25 5 53130
25 7 480700
25 9 2042975
25 11 4457400
25 13 5200300
25 15 3268760
25 17 1081575
Beta Function
15 Values
1.0 1.0 1.000000
0.2 1.0 5.000000
1.0 0.2 5.000000
0.4 1.0 2.500000
1.0 0.4 2.500000
0.6 1.0 1.666667
0.8 1.0 1.250000
6.0 6.0 3.607504E-04
6.0 5.0 7.936508E-04
6.0 4.0 1.984127E-03
6.0 3.0 5.952381E-03
6.0 2.0 0.238095E-01
7.0 7.0 8.325008E-05
5.0 5.0 1.587302E-03
4.0 4.0 7.142857E-03
3.0 3.0 0.333333E-01
2.0 2.0 1.666667E-01
Incomplete Gamma Function
20 Values
0.1 3.1622777E-02 0.7420263
0.1 3.1622777E-01 0.9119753
0.1 1.5811388 0.9898955
0.5 7.0710678E-02 0.2931279
0.5 7.0710678E-01 0.7656418
0.5 3.5355339 0.9921661
1.0 0.1000000 0.0951626
1.0 1.0000000 0.6321206
1.0 5.0000000 0.9932621
1.1 1.0488088E-01 0.0757471
1.1 1.0488088 0.6076457
1.1 5.2440442 0.9933425
2.0 1.4142136E-01 0.0091054
2.0 1.4142136 0.4130643
2.0 7.0710678 0.9931450
6.0 2.4494897 0.0387318
6.0 12.247449 0.9825937
11.0 16.583124 0.9404267
26.0 25.495098 0.4863866
41.0 44.821870 0.7359709
Error Function
20 Values
0.0 0.000000
0.1 0.1124629
0.2 0.2227026
0.3 0.3286268
0.4 0.4283924
0.5 0.5204999
0.6 0.6038561
0.7 0.6778012
0.8 0.7421010
0.9 0.7969082
1.0 0.8427008
1.1 0.8802051
1.2 0.9103140
1.3 0.9340079
1.4 0.9522851
1.5 0.9661051
1.6 0.9763484
1.7 0.9837905
1.8 0.9890905
1.9 0.9927904
Incomplete Beta Function
20 Values
0.5 0.5 0.01 0.0637686
0.5 0.5 0.10 0.2048328
0.5 0.5 1.00 1.0000000
1.0 0.5 0.01 0.0050126
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