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    Test of bessel functions 
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x = [0.01 0.535789 1.06158 1.58737 2.11316 2.63895 3.16474 3.69053 4.21632 4.74211 5.26789 5.79368 6.31947 6.84526 7.37105 7.89684 8.42263 8.94842 9.47421 10]
besselj(0, x) = [0.999975 0.92951 0.737496 0.462593 0.159139 -0.114928 -0.310723 -0.398702 -0.374249 -0.257398 -0.086903 0.0897353 0.227815 0.295737 0.281659 0.195053 0.06302 -0.0775296 -0.1897 -0.245936]
besselj(1, x) = [0.00499994 0.258396 0.459448 0.56861 0.56689 0.459775 0.275443 0.0577567 -0.144224 -0.287643 -0.34545 -0.31194 -0.203055 -0.0515029 0.10193 0.218652 0.271552 0.251069 0.166657 0.0434727]
besselj(5, x) = [2.60416e-14 1.13616e-05 0.000334941 0.00236109 0.00908689 0.0247775 0.0537407 0.0985326 0.158167 0.226989 0.294752 0.348121 0.373422 0.36004 0.30362 0.208143 0.0862016 -0.0428415 -0.156525 -0.234062]
besselj(0.3, x) = [0.227333 0.70974 0.733615 0.60061 0.371136 0.105291 -0.137641 -0.309029 -0.380002 -0.346362 -0.227881 -0.0621925 0.105129 0.231848 0.288953 0.266844 0.176472 0.0453878 -0.0901102 -0.194619]
besselj(1.7, x) = [7.9324e-05 0.0671604 0.198405 0.343409 0.457949 0.5077 0.475136 0.36316 0.194018 0.00362538 -0.167309 -0.28316 -0.321855 -0.279865 -0.172579 -0.0300451 0.110759 0.21514 0.259064 0.234648]
besselj(5.3, x) = [3.15929e-15 4.55312e-06 0.000165066 0.00131661 0.00554386 0.0162472 0.0374755 0.0725928 0.122628 0.184847 0.25211 0.313421 0.355752 0.366874 0.338539 0.269215 0.165544 0.0419839 -0.0814966 -0.183307]
bessely(0, x) = [-3.00546 -0.393388 0.134747 0.415986 0.518927 0.473687 0.320004 0.110022 -0.0997313 -0.259413 -0.335829 -0.318494 -0.220309 -0.0728078 0.0827225 0.205946 0.267362 0.254997 0.1764 0.0556712]
bessely(1, x) = [-63.6786 -1.38766 -0.7292 -0.355648 -0.0445541 0.204046 0.363724 0.416719 0.365013 0.231664 0.0556607 -0.117354 -0.245833 -0.301794 -0.276703 -0.182445 -0.0473107 0.0918537 0.199244 0.249015]
bessely(5, x) = [-2.44464e+12 -5637.1 -194.723 -28.527 -7.79607 -3.08477 -1.58367 -0.986094 -0.698192 -0.523538 -0.384929 -0.250859 -0.112548 0.0250994 0.148996 0.242846 0.292104 0.288391 0.232521 0.135403]
bessely(0.3, x) = [-4.50188 -0.756144 -0.192147 0.176734 0.399032 0.477286 0.4252 0.275829 0.0771929 -0.117613 -0.261894 -0.325212 -0.299154 -0.197723 -0.0524391 0.09649 0.210615 0.262704 0.242933 0.160422]
bessely(1.7, x) = [-2360.52 -3.009 -1.18556 -0.719724 -0.432942 -0.177942 0.0544787 0.240501 0.353307 0.377184 0.31416 0.184609 0.0227202 -0.131614 -0.242281 -0.285365 -0.254426 -0.161362 -0.0327734 0.0971924]
bessely(5.3, x) = [-1.90101e+13 -13261.1 -371.694 -47.9265 -11.8842 -4.32288 -2.05432 -1.19669 -0.809794 -0.599174 -0.453007 -0.323825 -0.193008 -0.0583251 0.0719857 0.183747 0.26139 0.292489 0.27158 0.202481]
besseli(0, x) = [1.00003 1.07307 1.30221 1.73636 2.46939 3.6625 5.58289 8.66847 13.6349 21.6517 34.6333 55.7173 90.0553 146.118 237.854 388.259 635.296 1041.7 1711.23 2815.72]
besseli(1, x) = [0.00500006 0.277623 0.609156 1.07134 1.76687 2.85419 4.58614 7.37227 11.8808 19.2059 31.1438 50.6486 82.5856 134.978 221.075 362.771 596.296 981.64 1618.23 2670.99]
besseli(5, x) = [2.60418e-14 1.16367e-05 0.000367922 0.00291285 0.0131853 0.0442943 0.124033 0.307911 0.702786 1.50928 3.0973 6.13946 11.8456 22.3731 41.5408 76.0692 137.725 247.025 439.607 777.188]
besseli(0.3, x) = [0.227342 0.792616 1.13369 1.61692 2.37007 3.56591 5.47561 8.53706 13.4628 21.4163 34.3012 55.2386 89.3537 145.076 236.289 385.889 631.678 1036.14 1702.64 2802.36]
besseli(1.7, x) = [7.93255e-05 0.0708274 0.244469 0.548134 1.05283 1.88426 3.25362 5.51145 9.23795 15.3932 25.5669 42.392 70.2338 116.333 192.706 319.311 529.31 877.838 1456.6 2418.23]
besseli(5.3, x) = [3.15932e-15 4.65805e-06 0.00018051 0.00160811 0.00790277 0.0282498 0.0830934 0.214721 0.506726 1.11937 2.35325 4.76284 9.35785 17.958 33.8151 62.6996 114.792 207.96 373.44 665.622]
besselk(0, x) = [4.72124 0.867728 0.385816 0.191022 0.0991824 0.0529157 0.0287345 0.0157986 0.0087668 0.0048996 0.00275388 0.00155503 0.000881465 0.000501281 0.000285867 0.000163415 9.36118e-05 5.37249e-05 3.08841e-05 1.77801e-05]
besselk(1, x) = [99.9739 1.51482 0.542899 0.244952 0.120671 0.0622273 0.032994 0.0178224 0.00975568 0.00539337 0.0030047 0.00168424 0.000948803 0.000536719 0.000304675 0.000173469 9.90207e-05 5.6651e-05 3.24749e-05 1.86488e-05]
besselk(5, x) = [3.83998e+12 8542.62 265.659 32.6729 6.97149 1.99175 0.679497 0.260647 0.108529 0.0479773 0.0221888 0.010627 0.00523225 0.00263412 0.00135049 0.00070292 0.000370528 0.000197424 0.000106162 5.75418e-05]