Sequences

392,541 sequences

sec(sin(arctanh(x)))=1+1/2!*x^2+9/4!*x^4+201/6!*x^6+7921/8!*x^8...A012061
sec(sin(arctanh(x)))=1+1/2!*x^2+9/4!*x^4+201/6!*x^6+7921/8!*x^8...
sech(sin(arctanh(x)))=1-1/2!*x^2+1/4!*x^4-1/6!*x^6+449/8!*x^8...A012062
sech(sin(arctanh(x)))=1-1/2!*x^2+1/4!*x^4-1/6!*x^6+449/8!*x^8...
exp(arcsin(arcsin(x)))=1+x+1/2!*x^2+3/3!*x^3+9/4!*x^4+49/5!*x^5...A012063
exp(arcsin(arcsin(x)))=1+x+1/2!*x^2+3/3!*x^3+9/4!*x^4+49/5!*x^5...
arcsin(arcsin(arcsin(x)))=x+3/3!*x^3+57/5!*x^5+2747/7!*x^7+249777/9!*x^9...A012064
arcsin(arcsin(arcsin(x)))=x+3/3!*x^3+57/5!*x^5+2747/7!*x^7+249777/9!*x^9...
Expansion of e.g.f. tan(arcsin(arcsin(x))).A012065
Expansion of e.g.f. tan(arcsin(arcsin(x))).
arctan(arcsin(arcsin(x)))=x+12/5!*x^5+248/7!*x^7+21648/9!*x^9...A012066
arctan(arcsin(arcsin(x)))=x+12/5!*x^5+248/7!*x^7+21648/9!*x^9...
cos(arcsin(arcsin(x)))=1-1/2!*x^2-7/4!*x^4-169/6!*x^6-8751/8!*x^8...A012067
cos(arcsin(arcsin(x)))=1-1/2!*x^2-7/4!*x^4-169/6!*x^6-8751/8!*x^8...
sinh(arcsin(arcsin(x)))=x+3/3!*x^3+49/5!*x^5+1963/7!*x^7+146017/9!*x^9...A012068
sinh(arcsin(arcsin(x)))=x+3/3!*x^3+49/5!*x^5+1963/7!*x^7+146017/9!*x^9...
arcsinh(arcsin(arcsin(x)))=x+1/3!*x^3+17/5!*x^5+561/7!*x^7+39521/9!*x^9...A012069
arcsinh(arcsin(arcsin(x)))=x+1/3!*x^3+17/5!*x^5+561/7!*x^7+39521/9!*x^9...
tanh(arcsin(arcsin(x)))=x+4/5!*x^5+136/7!*x^7+9424/9!*x^9...A012070
tanh(arcsin(arcsin(x)))=x+4/5!*x^5+136/7!*x^7+9424/9!*x^9...
arctanh(arcsin(arcsin(x)))=x+4/3!*x^3+92/5!*x^5+5160/7!*x^7+532880/9!*x^9...A012071
arctanh(arcsin(arcsin(x)))=x+4/3!*x^3+92/5!*x^5+5160/7!*x^7+532880/9!*x^9...
cosh(arcsin(arcsin(x)))=1+1/2!*x^2+9/4!*x^4+249/6!*x^6+14129/8!*x^8...A012072
cosh(arcsin(arcsin(x)))=1+1/2!*x^2+9/4!*x^4+249/6!*x^6+14129/8!*x^8...
sec(arcsin(arcsin(x)))=1+1/2!*x^2+13/4!*x^4+469/6!*x^6+32985/8!*x^8...A012073
sec(arcsin(arcsin(x)))=1+1/2!*x^2+13/4!*x^4+469/6!*x^6+32985/8!*x^8...
sech(arcsin(arcsin(x)))=1-1/2!*x^2-3/4!*x^4-69/6!*x^6-3335/8!*x^8...A012074
sech(arcsin(arcsin(x)))=1-1/2!*x^2-3/4!*x^4-69/6!*x^6-3335/8!*x^8...
Expansion of e.g.f.: exp(arcsin(tan(x)))=1+x+1/2!*x^2+4/3!*x^3+13/4!*x^4+76/5!*x^5...A012075
Expansion of e.g.f.: exp(arcsin(tan(x)))=1+x+1/2!*x^2+4/3!*x^3+13/4!*x^4+76/5!*x^5...
arcsin(arcsin(tan(x)))=x+4/3!*x^3+84/5!*x^5+4488/7!*x^7+458448/9!*x^9...A012076
arcsin(arcsin(tan(x)))=x+4/3!*x^3+84/5!*x^5+4488/7!*x^7+458448/9!*x^9...
tan(arcsin(tan(x))) = x+5/3!*x^3+121/5!*x^5+6845/7!*x^7+698161/9!*x^9...A012077
tan(arcsin(tan(x))) = x+5/3!*x^3+121/5!*x^5+6845/7!*x^7+698161/9!*x^9...
arctan(arcsin(tan(x)))=x+1/3!*x^3+9/5!*x^5+393/7!*x^7+33009/9!*x^9...A012078
arctan(arcsin(tan(x)))=x+1/3!*x^3+9/5!*x^5+393/7!*x^7+33009/9!*x^9...
cos(arcsin(tan(x)))=1-1/2!*x^2-11/4!*x^4-301/6!*x^6-16631/8!*x^8...A012079
cos(arcsin(tan(x)))=1-1/2!*x^2-11/4!*x^4-301/6!*x^6-16631/8!*x^8...
E.g.f.: sinh(arcsin(tan(x)))=x+4/3!*x^3+76/5!*x^5+3424/7!*x^7+285136/9!*x^9...A012080
E.g.f.: sinh(arcsin(tan(x)))=x+4/3!*x^3+76/5!*x^5+3424/7!*x^7+285136/9!*x^9...
arcsinh(arcsin(tan(x)))=x+2/3!*x^3+24/5!*x^5+888/7!*x^7+68352/9!*x^9...A012081
arcsinh(arcsin(tan(x)))=x+2/3!*x^3+24/5!*x^5+888/7!*x^7+68352/9!*x^9...
tanh(arcsin(tan(x)))=x+1/3!*x^3+1/5!*x^5+1/7!*x^7+7681/9!*x^9...A012082
tanh(arcsin(tan(x)))=x+1/3!*x^3+1/5!*x^5+1/7!*x^7+7681/9!*x^9...
arctanh(arcsin(tan(x)))=x+5/3!*x^3+129/5!*x^5+8133/7!*x^7+949281/9!*x^9...A012083
arctanh(arcsin(tan(x)))=x+5/3!*x^3+129/5!*x^5+8133/7!*x^7+949281/9!*x^9...
cosh(arcsin(tan(x)))=1+1/2!*x^2+13/4!*x^4+421/6!*x^6+26713/8!*x^8...A012084
cosh(arcsin(tan(x)))=1+1/2!*x^2+13/4!*x^4+421/6!*x^6+26713/8!*x^8...
Even coefficients in expansion of e.g.f. cos(x)/sqrt(cos(2*x)).A012085
Even coefficients in expansion of e.g.f. cos(x)/sqrt(cos(2*x)).
sech(arcsin(tan(x)))=1-1/2!*x^2-7/4!*x^4-121/6!*x^6-5167/8!*x^8...A012086
sech(arcsin(tan(x)))=1-1/2!*x^2-7/4!*x^4-121/6!*x^6-5167/8!*x^8...
Expansion of e.g.f.: exp(arcsin(arctan(x)))=1+x+1/2!*x^2-3/4!*x^4+4/5!*x^5+69/6!*x^6...A012087
Expansion of e.g.f.: exp(arcsin(arctan(x)))=1+x+1/2!*x^2-3/4!*x^4+4/5!*x^5+69/6!*x^6...
arcsin(arcsin(arctan(x)))=x+12/5!*x^5-88/7!*x^7+13968/9!*x^9...A012088
arcsin(arcsin(arctan(x)))=x+12/5!*x^5-88/7!*x^7+13968/9!*x^9...
Expansion of e.g.f. tan(arcsin(arctan(x))) (odd powers only).A012089
Expansion of e.g.f. tan(arcsin(arctan(x))) (odd powers only).
arctan(arcsin(arctan(x))) = x - 3/3!*x^3 + 57/5!*x^5 - 2587/7!*x^7 + 217137/9!*x^9 - ...A012090
arctan(arcsin(arctan(x))) = x - 3/3!*x^3 + 57/5!*x^5 - 2587/7!*x^7 + 217137/9!*x^9 - ...
cos(arcsin(arctan(x)))=1-1/2!*x^2+5/4!*x^4-109/6!*x^6+4521/8!*x^8...A012091
cos(arcsin(arctan(x)))=1-1/2!*x^2+5/4!*x^4-109/6!*x^6+4521/8!*x^8...
sinh(arcsin(arctan(x)))=x+4/5!*x^5-32/7!*x^7+1936/9!*x^9-67328/11!*x^11...A012092
sinh(arcsin(arctan(x)))=x+4/5!*x^5-32/7!*x^7+1936/9!*x^9-67328/11!*x^11...
arcsinh(arcsin(arctan(x)))=x-2/3!*x^3+32/5!*x^5-1224/7!*x^7+89984/9!*x^9...A012093
arcsinh(arcsin(arctan(x)))=x-2/3!*x^3+32/5!*x^5-1224/7!*x^7+89984/9!*x^9...
E.g.f.: tanh(arcsin(arctan(x))), odd powers only.A012094
E.g.f.: tanh(arcsin(arctan(x))), odd powers only.
arctanh(arcsin(arctan(x))) = x + 1/3!*x^3 + 17/5!*x^5 + 225/7!*x^7 + 19745/9!*x^9 + ...A012095
arctanh(arcsin(arctan(x))) = x + 1/3!*x^3 + 17/5!*x^5 + 225/7!*x^7 + 19745/9!*x^9 + ...
cosh(arcsin(arctan(x)))=1+1/2!*x^2-3/4!*x^4+69/6!*x^6-2503/8!*x^8...A012096
cosh(arcsin(arctan(x)))=1+1/2!*x^2-3/4!*x^4+69/6!*x^6-2503/8!*x^8...
Even coefficients in expansion of e.g.f. sec(arcsin(arctan(x))).A012097
Even coefficients in expansion of e.g.f. sec(arcsin(arctan(x))).
sech(arcsin(arctan(x)))=1-1/2!*x^2+9/4!*x^4-249/6!*x^6+13297/8!*x^8...A012098
sech(arcsin(arctan(x)))=1-1/2!*x^2+9/4!*x^4-249/6!*x^6+13297/8!*x^8...
Expansion of e.g.f.: exp(arcsin(sinh(x)))=1+x+1/2!*x^2+3/3!*x^3+9/4!*x^4+41/5!*x^5...A012099
Expansion of e.g.f.: exp(arcsin(sinh(x)))=1+x+1/2!*x^2+3/3!*x^3+9/4!*x^4+41/5!*x^5...
arcsin(arcsin(sinh(x)))=x+3/3!*x^3+49/5!*x^5+2187/7!*x^7+186337/9!*x^9...A012100
arcsin(arcsin(sinh(x)))=x+3/3!*x^3+49/5!*x^5+2187/7!*x^7+186337/9!*x^9...
Expansion of tan(arcsin(sinh(x))) (odd powers only).A012101
Expansion of tan(arcsin(sinh(x))) (odd powers only).
arctan(arcsin(sinh(x)))=x+4/5!*x^5+192/7!*x^7+9616/9!*x^9...A012102
arctan(arcsin(sinh(x)))=x+4/5!*x^5+192/7!*x^7+9616/9!*x^9...
cos(arcsin(sinh(x))) = 1-1/2!*x^2-7/4!*x^4-121/6!*x^6-5167/8!*x^8...A012103
cos(arcsin(sinh(x))) = 1-1/2!*x^2-7/4!*x^4-121/6!*x^6-5167/8!*x^8...
sinh(arcsin(sinh(x)))=x+3/3!*x^3+41/5!*x^5+1403/7!*x^7+90641/9!*x^9...A012104
sinh(arcsin(sinh(x)))=x+3/3!*x^3+41/5!*x^5+1403/7!*x^7+90641/9!*x^9...
arcsinh(arcsin(sinh(x)))=x+1/3!*x^3+9/5!*x^5+337/7!*x^7+20433/9!*x^9...A012105
arcsinh(arcsin(sinh(x)))=x+1/3!*x^3+9/5!*x^5+337/7!*x^7+20433/9!*x^9...
tanh(arcsin(sinh(x)))=x-4/5!*x^5+80/7!*x^7+5456/9!*x^9+511360/11!*x^11...A012106
tanh(arcsin(sinh(x)))=x-4/5!*x^5+80/7!*x^7+5456/9!*x^9+511360/11!*x^11...
arctanh(arcsin(sinh(x)))=x+4/3!*x^3+84/5!*x^5+4432/7!*x^7+432144/9!*x^9...A012107
arctanh(arcsin(sinh(x)))=x+4/3!*x^3+84/5!*x^5+4432/7!*x^7+432144/9!*x^9...
cosh(arcsin(sinh(x)))=1+1/2!*x^2+9/4!*x^4+201/6!*x^6+9649/8!*x^8...A012108
cosh(arcsin(sinh(x)))=1+1/2!*x^2+9/4!*x^4+201/6!*x^6+9649/8!*x^8...
sec(arcsin(sinh(x)))=1+1/2!*x^2+13/4!*x^4+421/6!*x^6+26713/8!*x^8...A012109
sec(arcsin(sinh(x)))=1+1/2!*x^2+13/4!*x^4+421/6!*x^6+26713/8!*x^8...
sech(arcsin(sinh(x)))=1-1/2!*x^2-3/4!*x^4-21/6!*x^6-1543/8!*x^8...A012110
sech(arcsin(sinh(x)))=1-1/2!*x^2-3/4!*x^4-21/6!*x^6-1543/8!*x^8...