1.8572024140248075150290504794684852507 E-10
1 - 1/46*x^2 + 1/4600*x^4 - 1/745200*x^6 + O(x^7)
besselh1
[1, 1]: error("incorrect type in isint (t_POL).")
[1, 2]: error("incorrect type in isint (t_POL).")
[1, 3]: error("incorrect type in isint (t_POL).")
[1, 4]: error("incorrect type in isint (t_POL).")
[2, 1]: 1 + (-1/4 - 1/2*I)*x^2 + (1/64 + 3/64*I)*x^4 + (-1/2304 - 11/6912*I)
*x^6 + O(x^7)
[2, 2]: 0.76519768655796655144971752610266322091 + 0.08825696421567695798292
6766023515162828*I
[2, 3]: 0.93846980724081290422840467359971262557 - 0.44451873350670655714839
847506833191038*I
[2, 4]: 0.22744989480229475542017649479538153049 - 0.05105545867308961813450
6215898455430057*I
[3, 1]: 4*I*x^-2 + (1 + I) + (-1/8 - 5/16*I)*x^2 + O(x^3)
[3, 2]: 0.44005058574493351595968220371891491313 - 0.78121282130028871654715
000004796482055*I
[3, 3]: 0.24226845767487388638395457614153164080 - 1.47147239267024306918858
46353232974532*I
[3, 4]: -0.015640669069980772062382408481746291203 - 0.292666506764257448350
36876789097604882*I
[4, 1]: (1 - I) + (-1/6 + 1/2*I)*x^2 + (1/120 - 1/24*I)*x^4 + (-1/5040 + 1/7
20*I)*x^6 + O(x^7)
[4, 2]: 0.67139670714180309041636401204046708054 - 0.43109886801837607952052
096729853340009*I
[4, 3]: 0.54097378993452809133091313466411641349 - 0.99024588024340488002335
195542348755756*I
[4, 4]: 0.14085110084956896263172093887132583804 - 0.20269003235062497321863
218183621826188*I
[5, 1]: error("domain error in besseln: 2n mod Z != 0")
[5, 2]: 0.26938214945091836540555327716757818205 - 1.03976259800634355895849
86807324939546*I
[5, 3]: 0.10940542017270712675781308031594165118 - 2.26083223277617932197371
42212172870084*I
[5, 4]: -0.19118520534054547001908105095911444129 - 0.3150944893490879685794
3764282485894340*I
[6, 1]: 380507258880*I*x^-20 + 10569646080*I*x^-18 + 165150720*I*x^-16 + O(x
^-15)
[6, 2]: 2.6306151236874532069978536877905029441 E-10 - 121618014.27868918928
813042666797114529*I
[6, 3]: 2.6131773608228030862436154291215029458 E-13 - 121963623349.56963053
464019824934463602*I
[6, 4]: -3689851.3824160519844673516400513272729 - 205195.348659968658569759
91788233215816*I
[7, 1]: error("domain error in besseln: 2n mod Z != 0")
[7, 2]: 0.58245577631758767297591196874548910891 - 1.44030896971971272914426
26374028590791*I
[7, 3]: 0.38021680508212671683351192801028812479 - 0.98141687216350076398947
866786133576037*I
[7, 4]: 0.20154312205360321787812231235059586177 - 0.76783553572168519458542
835586375224028*I
besselh2
[1, 1]: error("incorrect type in isint (t_POL).")
[1, 2]: error("incorrect type in isint (t_POL).")
[1, 3]: error("incorrect type in isint (t_POL).")
[1, 4]: error("incorrect type in isint (t_POL).")
[2, 1]: 1 + (-1/4 + 1/2*I)*x^2 + (1/64 - 3/64*I)*x^4 + (-1/2304 + 11/6912*I)
*x^6 + O(x^7)
[2, 2]: 0.76519768655796655144971752610266322091 - 0.08825696421567695798292
6766023515162828*I
[2, 3]: 0.93846980724081290422840467359971262557 + 0.44451873350670655714839
847506833191038*I
[2, 4]: 1.6477670588097637977792999000562559034 - 0.942004436545154646198413
22655202096895*I
[3, 1]: -4*I*x^-2 + (1 - I) + (-1/8 + 5/16*I)*x^2 + O(x^3)
[3, 2]: 0.44005058574493351595968220371891491313 + 0.78121282130028871654715
000004796482055*I
[3, 3]: 0.24226845767487388638395457614153164080 + 1.47147239267024306918858
46353232974532*I
[3, 4]: 1.2439613389157879924008217252327509830 + 1.022722564418433025377072
5711483489108*I
[4, 1]: (1 + I) + (-1/6 - 1/2*I)*x^2 + (1/120 + 1/24*I)*x^4 + (-1/5040 - 1/7
20*I)*x^6 + O(x^7)
[4, 2]: 0.67139670714180309041636401204046708054 + 0.43109886801837607952052
096729853340009*I
[4, 3]: 0.54097378993452809133091313466411641349 + 0.99024588024340488002335
195542348755756*I
[4, 4]: 1.7949514649306922611370433739385788319 + 0.323099244779188375242885
44204680075863*I
[5, 1]: error("domain error in besseln: 2n mod Z != 0")
[5, 2]: 0.26938214945091836540555327716757818205 + 1.03976259800634355895849
86807324939546*I
[5, 3]: 0.10940542017270712675781308031594165118 + 2.26083223277617932197371
42212172870084*I
[5, 4]: 0.79927619103677503777576265264156481050 + 1.08771932295608823645995
14526225738913*I
[6, 1]: -380507258880*I*x^-20 - 10569646080*I*x^-18 - 165150720*I*x^-16 + O(
x^-15)
[6, 2]: 2.6306151236874532069978536877905029441 E-10 + 121618014.27868918928
813042666797114529*I
[6, 3]: 2.6131773608228030862436154291215029458 E-13 + 121963623349.56963053
464019824934463602*I
[6, 4]: 3689851.3824160527671366489980962693903 + 205195.3486599858655861754
3080013707678*I
[7, 1]: error("domain error in besseln: 2n mod Z != 0")
[7, 2]: -0.053793008222511491987048146883432543616 + 0.334151434861435901321
42313893855556329*I
[7, 3]: -0.56713133425013005304402421178983091608 + 0.3472809452441059847447
3666211692428233*I
[7, 4]: 0.56669526894058228371774833075826997077 + 0.56952668509437225367197
037537154780157*I
besseli
[1, 1]: error("incorrect type in isint (t_POL).")
[1, 2]: error("incorrect type in isint (t_POL).")
[1, 3]: error("incorrect type in isint (t_POL).")
[1, 4]: error("incorrect type in isint (t_POL).")
[2, 1]: 1 + 1/4*x^2 + 1/64*x^4 + 1/2304*x^6 + O(x^7)
[2, 2]: 1.2660658777520083355982446252147175376
[2, 3]: 1.0634833707413235192631844154453565293
[2, 4]: 0.93760847680602927659973819742581871695 + 0.49652994760912213216645
972122523819950*I
[3, 1]: 1 + 1/8*x^2 + 1/192*x^4 + 1/9216*x^6 + O(x^7)
[3, 2]: 0.56515910399248502720769602760986330733
[3, 3]: 0.25789430539089631636247965952320963419
[3, 4]: 0.36502802882708778851335190162868643100 + 0.61416033492290361016921
965837550234589*I
[4, 1]: 1 + 1/6*x^2 + 1/120*x^4 + 1/5040*x^6 + O(x^7)
[4, 2]: 0.93767488824548764671726288439139336783
[4, 3]: 0.58799308679041632548887344016323449809
[4, 4]: 0.72698064596355457190337225790772836581 + 0.64183847533798587174998
976767935220305*I
[5, 1]: 1 + 0.10355339059327376220042218105242451964*x^2 + 0.003791260736238
8304125791589473295974330*x^4 + 7.1572974488511092712416929822558597732 E-5*
x^6 + O(x^7)
[5, 2]: 0.33140333780825958195735832301263837654
[5, 3]: 0.11521946070729671962775067900799783493
[5, 4]: 0.12322584912763267310364477086934931491 + 0.47591631113525426300712
693607959667758*I
[6, 1]: 1 + 1/44*x^2 + 1/4224*x^4 + 1/658944*x^6 + O(x^7)
[6, 2]: 2.7529480398368736252357102010027635344 E-10
[6, 3]: 2.6430419258812795384721773266572060848 E-13
[6, 4]: -3.9133464867902247105872448856946075458 E-10 + 8.603508207756458902
4593151718189946275 E-9*I
[7, 1]: 1 + (1/10 - 1/20*I)*x^2 + (1/320 - 1/320*I)*x^4 + (1/21760 - 1/13056
*I)*x^6 + O(x^7)
[7, 2]: 0.25369454079993178519197028239401935067 - 0.70438419774772610421577
993808361942912*I
[7, 3]: -0.10655105565636707643885659348968940182 - 0.3307637608360080173839
7259495461028707*I
[7, 4]: 0.47875240945839830415507917927631039129 + 0.07128046026390996971374
9689821284593892*I
besselj
[1, 1]: error("incorrect type in isint (t_POL).")
[1, 2]: error("incorrect type in isint (t_POL).")
[1, 3]: error("incorrect type in isint (t_POL).")
[1, 4]: error("incorrect type in isint (t_POL).")
[2, 1]: 1 - 1/4*x^2 + 1/64*x^4 - 1/2304*x^6 + O(x^7)
[2, 2]: 0.76519768655796655144971752610266322091
[2, 3]: 0.93846980724081290422840467359971262557
[2, 4]: 0.93760847680602927659973819742581871695 - 0.49652994760912213216645
972122523819950*I
[3, 1]: 1 - 1/8*x^2 + 1/192*x^4 - 1/9216*x^6 + O(x^7)
[3, 2]: 0.44005058574493351595968220371891491313
[3, 3]: 0.24226845767487388638395457614153164080
[3, 4]: 0.61416033492290361016921965837550234589 + 0.36502802882708778851335
190162868643100*I
[4, 1]: 1 - 1/6*x^2 + 1/120*x^4 - 1/5040*x^6 + O(x^7)
[4, 2]: 0.67139670714180309041636401204046708054
[4, 3]: 0.54097378993452809133091313466411641349
[4, 4]: 0.96790128289013061188438215640495233496 + 0.06020460621428170101212
6630105291248378*I
[5, 1]: 1 - 0.10355339059327376220042218105242451964*x^2 + 0.003791260736238
8304125791589473295974330*x^4 - 7.1572974488511092712416929822558597732 E-5*
x^6 + O(x^7)
[5, 2]: 0.26938214945091836540555327716757818205
[5, 3]: 0.10940542017270712675781308031594165118
[5, 4]: 0.30404549284811478387834080084122518461 + 0.38631241680350013394025
690489885747395*I
[6, 1]: 1 - 1/44*x^2 + 1/4224*x^4 - 1/658944*x^6 + O(x^7)
[6, 2]: 2.6306151236874532069978536877905029441 E-10
[6, 3]: 2.6131773608228030862436154291215029458 E-13
[6, 4]: 3.9133464867902247105872448856946075458 E-10 + 8.6035082077564589024
593151718189946275 E-9*I
[7, 1]: 1 + (-1/10 + 1/20*I)*x^2 + (1/320 - 1/320*I)*x^4 + (-1/21760 + 1/130
56*I)*x^6 + O(x^7)
[7, 2]: 0.26433138404753809049443191093102828265 - 0.55307876742913841391141
974923215175792*I
[7, 3]: -0.093457264584001668105256141889771395645 - 0.317067963459697389622
37100287220573902*I
[7, 4]: 0.38411919549709275079793532155443291627 - 0.09915442531365647045672
8990246102219357*I
besseljh
[1, 1]: error("incorrect type in jbesselh (t_POL).")
[1, 2]: error("incorrect type in jbesselh (t_POL).")
[1, 3]: error("incorrect type in jbesselh (t_POL).")
[1, 4]: error("incorrect type in jbesselh (t_POL).")
[2, 1]: 1 - 1/6*x^2 + 1/120*x^4 - 1/5040*x^6 + O(x^7)
[2, 2]: 0.67139670714180309041636401204046708055
[2, 3]: 0.54097378993452809133091313466411641349
[2, 4]: 0.96790128289013061188438215640495233496 + 0.06020460621428170101212
6630105291248379*I
[3, 1]: 1 - 1/10*x^2 + 1/280*x^4 - 1/15120*x^6 + O(x^7)
[3, 2]: 0.24029783912342701089584304474193368046
[3, 3]: 0.091701699625651302638474313904745269419
[3, 4]: 0.25115830598729948221749558131361228142 + 0.37320184370263719381653
345438379595363*I
[4, 1]: error("incorrect type in jbesselh (t_FRAC).")
[4, 2]: error("incorrect type in jbesselh (t_FRAC).")
[4, 3]: error("incorrect type in jbesselh (t_FRAC).")
[4, 4]: error("incorrect type in jbesselh (t_FRAC).")
[5, 1]: error("incorrect type in jbesselh (t_REAL).")
[5, 2]: error("incorrect type in jbesselh (t_REAL).")
[5, 3]: error("incorrect type in jbesselh (t_REAL).")
[5, 4]: error("incorrect type in jbesselh (t_REAL).")
[6, 1]: 1 - 1/46*x^2 + 1/4600*x^4 - 1/745200*x^6 + O(x^7)
[6, 2]: 5.6781874776346222994224383562334313034 E-11
[6, 3]: 3.9855051571881421614590449651836245138 E-14
[6, 4]: -7.5567733209249243890627329164720828368 E-10 + 2.075203626533608360
9444796696375043842 E-9*I
[7, 1]: error("incorrect type in jbesselh (t_COMPLEX).")
[7, 2]: error("incorrect type in jbesselh (t_COMPLEX).")
[7, 3]: error("incorrect type in jbesselh (t_COMPLEX).")
[7, 4]: error("incorrect type in jbesselh (t_COMPLEX).")
besselk
[1, 1]: error("incorrect type in isint (t_POL).")
[1, 2]: error("incorrect type in isint (t_POL).")
[1, 3]: error("incorrect type in isint (t_POL).")
[1, 4]: error("incorrect type in isint (t_POL).")
[2, 1]: 1/2*x^2 + 3/64*x^4 + 11/6912*x^6 + O(x^7)
[2, 2]: 0.42102443824070833333562737921260903614
[2, 3]: 0.92441907122766586178192416753021698954
[2, 4]: 0.080197726946517818726968736564279166834 - 0.3572774592853302506059
4569325002398166*I
[3, 1]: -4*x^-2 + 1 + 5/16*x^2 + O(x^3)
[3, 2]: 0.60190723019723457473754000153561733926
[3, 3]: 1.6564411200033008936964454031740915115
[3, 4]: 0.024568305523740348612477346185201235995 - 0.4597194738011893647760
4300851857199811*I
[4, 1]: 1/2*x^-1 - 1 + 1/4*x - 1/6*x^2 + 1/48*x^3 - 1/120*x^4 + O(x^5)
[4, 2]: 0.46106850444789455843957587387569458969
[4, 3]: 1.0750476034999202387227558602482085118
[4, 4]: 0.068685783419996419480057426969766668173 - 0.3815782598126830739602
7449697029326916*I
[5, 1]: error("domain error in besselk: 2n mod Z != 0")
[5, 2]: 0.84808712130706055249297377794312403937
[5, 3]: 2.8356740750874926233948621504947623564
[5, 4]: -0.060833677914566850837201614245364256444 - 0.575727321703454299901
71626792018756559*I
[6, 1]: 380507258880*x^-20 - 10569646080*x^-18 + 165150720*x^-16 + O(x^-15)
[6, 2]: 180713289.90102945469159786130234001591
[6, 3]: 188937569319.90025964462417816833870273
[6, 4]: -322320.09995047688108832869622332914303 - 5796004.99791820584997486
34606037942199*I
[7, 1]: error("domain error in besselk: 2n mod Z != 0")
[7, 2]: 0.32545977186584141085464640324923711950 + 0.28942803702599212763456
715924152302743*I
[7, 3]: 0.38335176781651847215073123333424046030 + 0.96679218008775594813220
288497987441030*I
[7, 4]: 0.31594457269950863123935043154373419884 - 0.40665811731437652111601
397817696670098*I
besseln
[1, 1]: error("incorrect type in isint (t_POL).")
[1, 2]: error("incorrect type in isint (t_POL).")
[1, 3]: error("incorrect type in isint (t_POL).")
[1, 4]: error("incorrect type in isint (t_POL).")
[2, 1]: -1/2*x^2 + 3/64*x^4 - 11/6912*x^6 + O(x^7)
[2, 2]: 0.088256964215676957982926766023515162828
[2, 3]: -0.44451873350670655714839847506833191038
[2, 4]: 0.44547448893603251403195350532678276945 + 0.71015858200373452117956
170263043718646*I
[3, 1]: 4*x^-2 + 1 - 5/16*x^2 + O(x^3)
[3, 2]: -0.78121282130028871654715000004796482055
[3, 3]: -1.4714723926702430691885846353232974532
[3, 4]: -0.65769453559134523686372066951966247983 + 0.6298010039928843822316
0206685724863709*I
[4, 1]: -1 + 1/2*x^2 - 1/24*x^4 + 1/720*x^6 + O(x^7)
[4, 2]: -0.43109886801837607952052096729853340009
[4, 3]: -0.99024588024340488002335195542348755756
[4, 4]: -0.26289463856490667423075881194150951025 + 0.8270501820405616492526
6121753362649691*I
[5, 1]: error("domain error in besseln: 2n mod Z != 0")
[5, 2]: -1.0397625980063435589584986807324939546
[5, 3]: -2.2608322327761793219737142212172870084
[5, 4]: -0.70140690615258810251969454772371641734 + 0.4952306981886602538974
2185180033962590*I
[6, 1]: 380507258880*x^-20 + 10569646080*x^-18 + 165150720*x^-16 + O(x^-15)
[6, 2]: -121618014.27868918928813042666797114529
[6, 3]: -121963623349.56963053464019824934463602
[6, 4]: -205195.34865997726207796767434123461747 + 3689851.38241605237580200
03190737983316*I
[7, 1]: error("domain error in besseln: 2n mod Z != 0")
[7, 2]: -0.88723020229057431523284288817070732122 - 0.3181243922700495824814
8005781446082626*I
[7, 3]: -0.66434890870380337436710766498913002135 - 0.4736740696661283849387
6806990005952043*I
[7, 4]: -0.66868111040802872412869936561765002092 + 0.1825760734434895329198
1300920383705450*I
[0.38318604387456485808270441031554362199 - 1.130318207984970054415392055219
7266147*I, -0.38318604387456485808270441031554362199 + 0.E-38*I]~
[-0.38318604387456485808270441031554362199 + 0.E-38*I, 0.3831860438745648580
8270441031554362199 + 1.1303182079849700544153920552197266147*I]~
[0.E-39 - 0.44005058574493351595968220371891491313*I, 0.E-39 + 0.44005058574
493351595968220371891491313*I]~
[0.E-38 - 0.56515910399248502720769602760986330733*I, 0.E-38 + 0.56515910399
248502720769602760986330733*I]~
[-0.20755374871029735167013412472066868268 - 0.20755374871029735167013412472
066868268*I, -0.20755374871029735167013412472066868268 + 0.20755374871029735
167013412472066868268*I]~
[-0.69122984369208426288314166384697051872 + 1.22712623014357148924328078170
72674867*I, -0.69122984369208426288314166384697051872 - 1.227126230143571489
2432807817072674867*I]~
[-0.56515910399248502720769602760986330733 - 0.38318604387456485808270441031
554362199*I, -0.56515910399248502720769602760986330733 + 0.38318604387456485
808270441031554362199*I]~
[0.44005058574493351595968220371891491313 - 0.781212821300288716547150000047
96482055*I]
[0.44005058574493351595968220371891491313 + 0.781212821300288716547150000047
96482055*I]
[0.56515910399248502720769602760986330733]
[0.44005058574493351595968220371891491313]
[0.24029783912342701089584304474193368046]
[0.60190723019723457473754000153561733926]
[-0.78121282130028871654715000004796482055]
[0.44005058574493351595968220371891491313 - 0.781212821300288716547150000047
96482055*I]~
[0.44005058574493351595968220371891491313 + 0.781212821300288716547150000047
96482055*I]~
[0.56515910399248502720769602760986330733]~
[0.44005058574493351595968220371891491313]~
[0.24029783912342701089584304474193368046]~
[0.60190723019723457473754000153561733926]~
[-0.78121282130028871654715000004796482055]~
Mat(0.44005058574493351595968220371891491313 - 0.781212821300288716547150000
04796482055*I)
Mat(0.44005058574493351595968220371891491313 + 0.781212821300288716547150000
04796482055*I)
Mat(0.56515910399248502720769602760986330733)
Mat(0.44005058574493351595968220371891491313)
Mat(0.24029783912342701089584304474193368046)
Mat(0.60190723019723457473754000153561733926)
Mat(-0.78121282130028871654715000004796482055)
0.E-96
5.3192304053524357058659474657917582463 E-127
2.0125228237125015700004500237283661172 E-436
5.7412378153505365740198971395908944617 E-10
2.0105123109834969409015328783614871604 E-436 + 0.E-475*I
11.628856980944362293418444710423341176
Total time spent: 24
