A012530
arctanh(sinh(x)*sin(x)) = 2/2!*x^2+232/6!*x^6+685472/10!*x^10...
Original entry on oeis.org
2, 232, 685472, 11496925312, 641870470410752, 90115671250751137792, 26741121618547455928082432, 14898765702188922919730883100672, 14301272675149517137926114108443328512, 22156614594176569412220482693952524899581952
Offset: 0
Patrick Demichel (patrick.demichel(AT)hp.com)
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Table[n!*SeriesCoefficient[ArcTanh[Sinh[x]*Sin[x]],{x,0,n}],{n,2,40,4}] (* Vaclav Kotesovec, Nov 02 2013 *)
A024275
E.g.f: log(1+sinh(x)*sin(x))/2 (even powers only).
Original entry on oeis.org
0, 1, -6, 116, -4816, 342736, -37272576, 5748462656, -1193465153536, 320935235205376, -108513125117853696, 45057835625375568896, -22540295648947188269056, 13370560809273727964041216
Offset: 0
log(1+sinh(x)*sin(x))/2 = 0 + 1/2*x^2 - 1/4*x^4 + 29/180*x^6 - 43/360*x^8 + 21421/226800*x^10 +- ... .
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With[{nn=30},Take[CoefficientList[Series[Log[1+Sinh[x]*Sin[x]]/2,{x,0,nn}],x] Range[0,nn]!,{1,-1,2}]] (* Harvey P. Dale, Mar 01 2019 *)
Extended with signs, Mar 1997
A296622
Expansion of e.g.f. log(1 + arcsin(x)*arcsinh(x)) (even powers only).
Original entry on oeis.org
0, 2, -12, 328, -15008, 1356192, -166628352, 31500831360, -7474571071488, 2418220114014720, -940432709166170112, 464609611973533501440, -268355615175956213268480, 188067307050238642631516160, -151072053399934628129585233920, 142618740583722182161589570273280
Offset: 0
log(1 + arcsin(x)*arcsinh(x)) = 2*x^2/2! - 12*x^4/4! + 328*x^6/6! - 15008*x^8/8! + 1356192*x^10/10! - 166628352*x^12/12! + ...
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nmax = 15; Table[(CoefficientList[Series[Log[1 + ArcSin[x] ArcSinh[x]], {x, 0, 2 nmax}], x] Range[0, 2 nmax]!)[[n]], {n, 1, 2 nmax + 1, 2}]
nmax = 15; Table[(CoefficientList[Series[Log[1 - I Log[I x + Sqrt[1 - x^2]] Log[x + Sqrt[1 + x^2]]], {x, 0, 2 nmax}], x] Range[0, 2 nmax]!)[[n]], {n, 1, 2 nmax + 1, 2}]
Showing 1-3 of 3 results.