A096718
Denominators of terms in series expansion of arcsin(arctan(x)).
Original entry on oeis.org
1, 6, 120, 5040, 362880, 4435200, 32947200, 145297152000, 69701632000, 13516122267648000, 5676771352412160000, 2872446304320552960000, 1723467782592331776000000, 1935799013407707050803200, 485144691014524112732160000, 1353553687930522274522726400000, 204193242064947360270857011200000
Offset: 0
arcsin(arctan(x)) = x - 1/6*x^3 + 13/120*x^5 - 341/5040*x^7 + 18649/362880*x^9 - 177761/4435200*x^11 + ...
-
Denominator[Take[CoefficientList[Series[ArcSin[ArcTan[x]], {x,0,40}], x], {2,-1,2}]] (* G. C. Greubel, Nov 17 2016 *)
A096717
Numerators of terms in series expansion of arcsin(arctan(x)).
Original entry on oeis.org
1, -1, 13, -341, 18649, -177761, 1087433, -4043494549, 1674761567, -284891766539657, 106410874319325461, -48402125366670946877, 26344930021064765797249, -27048608191991004321089, 6237195766537863970288933, -16102066950215127630856787159, 2258820895862623437612519923989
Offset: 0
arcsin(arctan(x)) = x - 1/6*x^3 + 13/120*x^5 - 341/5040*x^7 + 18649/362880*x^9 - 177761/4435200*x^11 + ...
Cf.
A096718,
A096664,
A096671,
A096712,
A096716,
A045688,
A045689,
A096719,
A096720,
A096721,
A096722.
-
Numerator[Take[CoefficientList[Series[ArcSin[ArcTan[x]], {x,0,50}], x], {2, -1, 2}]] (* G. C. Greubel, Nov 17 2016 *)
A096721
Numerators of terms in series expansion of arcsin(arctan(x)) - arctan(arcsin(x)).
Original entry on oeis.org
0, 0, 0, -1, 13, -2329, 3749, -1405132357, 41223659, -3230487913, 87420689313263, -92876785811395309, 6545378422138547141, -76226954122169434345117, 13717355610784766550119, -152042860419225571514252591, 325359516347299085987218014617, -501994552683503696983628163720749, 226141284010354023120430917899293
Offset: 0
arcsin(arctan(x)) - arctan(arcsin(x)) = -1/30*x^7 + 13/756*x^9 - 2329/75600*x^11 + 3749/199584*x^13 - 1405132357/54486432000*x^15 + ...
Cf.
A096722,
A096717,
A096718,
A096664,
A096671,
A096712,
A096716,
A045688,
A045689,
A096719,
A096720.
-
With[{nn=40},Numerator[Take[CoefficientList[Series[ArcSin[ArcTan[x]] - ArcTan[ArcSin[x]],{x,0,nn}],x],{2,-1,2}]]] (* Harvey P. Dale, Dec 07 2011 *)
A096725
Numerators of terms in series expansion of (sin(tan(x)) - tan(sin(x))) / (arcsin(arctan(x)) - arctan(arcsin(x))).
Original entry on oeis.org
1, 5, 1313, -2773, -701933647, -86849082293, -174426488476171, -130176915706274917, -42426469007472079018663, -24495552034235134641205327, -3019410235003955483667737236843, -74265172933666226350348992663473, -2457268368880426576340457161112391, -589361165665450343618737576026916723726003
Offset: 0
(sin(tan(x)) - tan(sin(x))) / (arcsin(arctan(x)) - arctan(arcsin(x))) = 1 + 5/3*x^2 + 1313/1890*x^4 - 2773/11907*x^6 - 701933647/1650310200*x^8 - 86849082293/270320810760*x^10 - ...
- V. I. Arnold, Huygens and Barrow, Newton and Hooke, Birkhäuser, Basel, 1990.
Cf.
A096730,
A096722,
A096717,
A096718,
A096664,
A096671,
A096712,
A096716,
A045688,
A045689,
A096719,
A096720.
-
Numerator[Take[CoefficientList[Series[(Sin[Tan[x]] - Tan[Sin[x]]) / (ArcSin[ArcTan[x]] - ArcTan[ArcSin[x]]), {x,0,50}], x], {1, -1, 2}]] (* G. C. Greubel, Nov 20 2016 *)
A096730
Denominators of terms in series expansion of (sin(tan(x)) - tan(sin(x))) / (arcsin(arctan(x)) - arctan(arcsin(x))).
Original entry on oeis.org
1, 3, 1890, 11907, 1650310200, 270320810760, 851510553894000, 1003164583542521400, 480315202600159246320000, 393378150929530422736080000, 62700543476657854079903791200000, 1975067119514722403516969422800000, 76571832941186160874811737622400000
Offset: 0
(sin(tan(x)) - tan(sin(x))) / (arcsin(arctan(x)) - arctan(arcsin(x))) = 1 + 5/3*x^2 + 1313/1890*x^4 - 2773/11907*x^6 - 701933647/1650310200*x^8 - 86849082293/270320810760*x^10 - ...
- V. I. Arnold, Huygens and Barrow, Newton and Hooke, Birkhäuser, Basel, 1990.
Cf.
A096725,
A096722,
A096717,
A096718,
A096664,
A096671,
A096712,
A096716,
A045688,
A045689,
A096719,
A096720.
-
Denominator[Take[CoefficientList[Series[(Sin[Tan[x]] - Tan[Sin[x]]) / (ArcSin[ArcTan[x]] - ArcTan[ArcSin[x]]), {x, 0, 10}], x], {1, -1, 2}]] (* G. C. Greubel, Nov 20 2016 *)
Showing 1-5 of 5 results.