Sequences

392,541 sequences

Expansion of e.g.f. arcsinh(sin(sin(x))), odd powers only.A012011
Expansion of e.g.f. arcsinh(sin(sin(x))), odd powers only.
sec(sin(sin(x)))=1+1/2!*x^2-3/4!*x^4-27/6!*x^6+1145/8!*x^8...A012012
sec(sin(sin(x)))=1+1/2!*x^2-3/4!*x^4-27/6!*x^6+1145/8!*x^8...
sech(sin(sin(x)))=1-1/2!*x^2+13/4!*x^4-373/6!*x^6+19545/8!*x^8...A012013
sech(sin(sin(x)))=1-1/2!*x^2+13/4!*x^4-373/6!*x^6+19545/8!*x^8...
arctan(sin(tan(x)))=x-1/3!*x^3+1/5!*x^5-169/7!*x^7-1823/9!*x^9...A012014
arctan(sin(tan(x)))=x-1/3!*x^3+1/5!*x^5-169/7!*x^7-1823/9!*x^9...
arcsinh(sin(tan(x)))=x-4/5!*x^5-192/7!*x^7-7600/9!*x^9-507136/11!*x^11...A012015
arcsinh(sin(tan(x)))=x-4/5!*x^5-192/7!*x^7-7600/9!*x^9-507136/11!*x^11...
arctanh(sin(tan(x)))=x+3/3!*x^3+41/5!*x^5+1299/7!*x^7+74609/9!*x^9...A012016
arctanh(sin(tan(x)))=x+3/3!*x^3+41/5!*x^5+1299/7!*x^7+74609/9!*x^9...
sec(sin(tan(x)))=1+1/2!*x^2+9/4!*x^4+153/6!*x^6+2993/8!*x^8...A012017
sec(sin(tan(x)))=1+1/2!*x^2+9/4!*x^4+153/6!*x^6+2993/8!*x^8...
sech(sin(tan(x)))=1-1/2!*x^2+1/4!*x^4+47/6!*x^6+897/8!*x^8...A012018
sech(sin(tan(x)))=1-1/2!*x^2+1/4!*x^4+47/6!*x^6+897/8!*x^8...
E.g.f.: exp(sin(arctan(x))).A012019
E.g.f.: exp(sin(arctan(x))).
Expansion of e.g.f.: sin(sin(arctan(x))) (odd powers only).A012020
Expansion of e.g.f.: sin(sin(arctan(x))) (odd powers only).
Expansion of e.g.f.: tan(sin(arctan(x))) (odd powers only).A012021
Expansion of e.g.f.: tan(sin(arctan(x))) (odd powers only).
Expansion of e.g.f.: arctan(sin(arctan(x))) (odd powers only).A012022
Expansion of e.g.f.: arctan(sin(arctan(x))) (odd powers only).
Expansion of e.g.f. cos(sin(arctan(x))) (even powers).A012023
Expansion of e.g.f. cos(sin(arctan(x))) (even powers).
E.g.f. sinh(sin(arctan(x))) (odd powers only).A012024
E.g.f. sinh(sin(arctan(x))) (odd powers only).
E.g.f. arcsinh(sin(arctan(x))) = arcsinh(x/(1+x^2)^(1/2)) (odd powers only).A012025
E.g.f. arcsinh(sin(arctan(x))) = arcsinh(x/(1+x^2)^(1/2)) (odd powers only).
Expansion of e.g.f. tanh(sin(arctan(x))) = tanh(x/sqrt(1+x^2)) (odd powers only).A012026
Expansion of e.g.f. tanh(sin(arctan(x))) = tanh(x/sqrt(1+x^2)) (odd powers only).
E.g.f. cosh(sin(arctan(x))) = cosh(x/sqrt(1+x^2)) (even powers only).A012027
E.g.f. cosh(sin(arctan(x))) = cosh(x/sqrt(1+x^2)) (even powers only).
Expansion of e.g.f. sec(sin(arctan(x))) = 1/cos(x/sqrt(1+x^2)) (even powers only).A012028
Expansion of e.g.f. sec(sin(arctan(x))) = 1/cos(x/sqrt(1+x^2)) (even powers only).
E.g.f.: sech(sin(arctan(x))) (even powers only).A012029
E.g.f.: sech(sin(arctan(x))) (even powers only).
arctan(sin(sinh(x))) = x - 2/3!*x^3 +16/5!*x^5 - 440/7!*x^7 + 20224/9!*x^9 - ....A012030
arctan(sin(sinh(x))) = x - 2/3!*x^3 +16/5!*x^5 - 440/7!*x^7 + 20224/9!*x^9 - ....
arcsinh(sin(sinh(x)))=x-1/3!*x^3+1/5!*x^5-113/7!*x^7+4033/9!*x^9...A012031
arcsinh(sin(sinh(x)))=x-1/3!*x^3+1/5!*x^5-113/7!*x^7+4033/9!*x^9...
sec(sin(sinh(x)))=1+1/2!*x^2+5/4!*x^4+13/6!*x^6-1303/8!*x^8...A012032
sec(sin(sinh(x)))=1+1/2!*x^2+5/4!*x^4+13/6!*x^6-1303/8!*x^8...
sech(sin(sinh(x)))=1-1/2!*x^2+5/4!*x^4-13/6!*x^6-407/8!*x^8...A012033
sech(sin(sinh(x)))=1-1/2!*x^2+5/4!*x^4-13/6!*x^6-407/8!*x^8...
exp(sin(arcsinh(x))) = 1+x+1/2!*x^2-1/3!*x^3-7/4!*x^4+1/5!*x^5...A012034
exp(sin(arcsinh(x))) = 1+x+1/2!*x^2-1/3!*x^3-7/4!*x^4+1/5!*x^5...
sin(sin(arcsinh(x))) = x-3/3!*x^3+41/5!*x^5-1291/7!*x^7+73169/9!*x^9...A012035
sin(sin(arcsinh(x))) = x-3/3!*x^3+41/5!*x^5-1291/7!*x^7+73169/9!*x^9...
tan(sin(arcsinh(x)))=x-4/5!*x^5+32/7!*x^7+80/9!*x^9-34048/11!*x^11...A012036
tan(sin(arcsinh(x)))=x-4/5!*x^5+32/7!*x^7+80/9!*x^9-34048/11!*x^11...
arctan(sin(arcsinh(x)))=x-4/3!*x^3+84/5!*x^5-4320/7!*x^7+410640/9!*x^9...A012037
arctan(sin(arcsinh(x)))=x-4/3!*x^3+84/5!*x^5-4320/7!*x^7+410640/9!*x^9...
cos(sin(arcsinh(x)))=1-1/2!*x^2+9/4!*x^4-201/6!*x^6+8753/8!*x^8...A012038
cos(sin(arcsinh(x)))=1-1/2!*x^2+9/4!*x^4-201/6!*x^6+8753/8!*x^8...
sinh(sin(arcsinh(x))) = x-1/3!*x^3+1/5!*x^5+111/7!*x^7-9407/9!*x^9...A012039
sinh(sin(arcsinh(x))) = x-1/3!*x^3+1/5!*x^5+111/7!*x^7-9407/9!*x^9...
arcsinh(sin(arcsinh(x)))=x-3/3!*x^3+49/5!*x^5-2075/7!*x^7+168865/9!*x^9...A012040
arcsinh(sin(arcsinh(x)))=x-3/3!*x^3+49/5!*x^5-2075/7!*x^7+168865/9!*x^9...
tanh(sin(arcsinh(x)))=x-4/3!*x^3+76/5!*x^5-3312/7!*x^7+255952/9!*x^9...A012041
tanh(sin(arcsinh(x)))=x-4/3!*x^3+76/5!*x^5-3312/7!*x^7+255952/9!*x^9...
arctanh(sin(arcsinh(x)))=x+4/5!*x^5-80/7!*x^7+4240/9!*x^9-342400/11!*x^11...A012042
arctanh(sin(arcsinh(x)))=x+4/5!*x^5-80/7!*x^7+4240/9!*x^9-342400/11!*x^11...
cosh(sin(arcsinh(x))) = 1+1/2!*x^2-7/4!*x^4+121/6!*x^6-4271/8!*x^8...A012043
cosh(sin(arcsinh(x))) = 1+1/2!*x^2-7/4!*x^4+121/6!*x^6-4271/8!*x^8...
sec(sin(arcsinh(x)))=1+1/2!*x^2-3/4!*x^4+21/6!*x^6-647/8!*x^8...A012044
sec(sin(arcsinh(x)))=1+1/2!*x^2-3/4!*x^4+21/6!*x^6-647/8!*x^8...
sech(sin(arcsinh(x)))=1-1/2!*x^2+13/4!*x^4-421/6!*x^6+25817/8!*x^8...A012045
sech(sin(arcsinh(x)))=1-1/2!*x^2+13/4!*x^4-421/6!*x^6+25817/8!*x^8...
arctan(sin(tanh(x)))=x-5/3!*x^3+121/5!*x^5-7013/7!*x^7+752785/9!*x^9...A012046
arctan(sin(tanh(x)))=x-5/3!*x^3+121/5!*x^5-7013/7!*x^7+752785/9!*x^9...
arcsinh(sin(tanh(x)))=x-4/3!*x^3+76/5!*x^5-3536/7!*x^7+317392/9!*x^9...A012047
arcsinh(sin(tanh(x)))=x-4/3!*x^3+76/5!*x^5-3536/7!*x^7+317392/9!*x^9...
arctanh(sin(tanh(x)))=x-1/3!*x^3+1/5!*x^5+55/7!*x^7-2207/9!*x^9...A012048
arctanh(sin(tanh(x)))=x-1/3!*x^3+1/5!*x^5+55/7!*x^7-2207/9!*x^9...
sec(sin(tanh(x))) = 1+1/2!*x^2-7/4!*x^4+73/6!*x^6+209/8!*x^8...A012049
sec(sin(tanh(x))) = 1+1/2!*x^2-7/4!*x^4+73/6!*x^6+209/8!*x^8...
sech(sin(tanh(x)))=1-1/2!*x^2+17/4!*x^4-673/6!*x^6+48481/8!*x^8...A012050
sech(sin(tanh(x)))=1-1/2!*x^2+17/4!*x^4-673/6!*x^6+48481/8!*x^8...
exp(sin(arctanh(x)))=1+x+1/2!*x^2+2/3!*x^3+5/4!*x^4+16/5!*x^5...A012051
exp(sin(arctanh(x)))=1+x+1/2!*x^2+2/3!*x^3+5/4!*x^4+16/5!*x^5...
sin(sin(arctanh(x)))=x-4/5!*x^5-136/7!*x^7-7408/9!*x^9-644416/11!*x^11...A012052
sin(sin(arctanh(x)))=x-4/5!*x^5-136/7!*x^7-7408/9!*x^9-644416/11!*x^11...
tan(sin(arctanh(x)))=x+3/3!*x^3+41/5!*x^5+1187/7!*x^7+54449/9!*x^9...A012053
tan(sin(arctanh(x)))=x+3/3!*x^3+41/5!*x^5+1187/7!*x^7+54449/9!*x^9...
arctan(sin(arctanh(x)))=x-1/3!*x^3+9/5!*x^5-225/7!*x^7+3345/9!*x^9...A012054
arctan(sin(arctanh(x)))=x-1/3!*x^3+9/5!*x^5-225/7!*x^7+3345/9!*x^9...
cos(sin(arctanh(x)))=1-1/2!*x^2-3/4!*x^4-21/6!*x^6+185/8!*x^8...A012055
cos(sin(arctanh(x)))=1-1/2!*x^2-3/4!*x^4-21/6!*x^6+185/8!*x^8...
sinh(sin(arctanh(x)))=x+2/3!*x^3+16/5!*x^5+216/7!*x^7-1280/9!*x^9...A012056
sinh(sin(arctanh(x)))=x+2/3!*x^3+16/5!*x^5+216/7!*x^7-1280/9!*x^9...
arcsinh(sin(arctanh(x)))=x+4/5!*x^5-80/7!*x^7-3440/9!*x^9-764800/11!*x^11...A012057
arcsinh(sin(arctanh(x)))=x+4/5!*x^5-80/7!*x^7-3440/9!*x^9-764800/11!*x^11...
tanh(sin(arctanh(x)))=x-1/3!*x^3+1/5!*x^5-57/7!*x^7-3167/9!*x^9...A012058
tanh(sin(arctanh(x)))=x-1/3!*x^3+1/5!*x^5-57/7!*x^7-3167/9!*x^9...
arctanh(sin(arctanh(x))) = x + (3/3!)*x^3 + (49/5!)*x^5 + (1915/7!)*x^7 + (136225/9!)*x^9 + ...A012059
arctanh(sin(arctanh(x))) = x + (3/3!)*x^3 + (49/5!)*x^5 + (1915/7!)*x^7 + (136225/9!)*x^9 + ...
cosh(sin(arctanh(x)))=1+1/2!*x^2+5/4!*x^4+61/6!*x^6+937/8!*x^8...A012060
cosh(sin(arctanh(x)))=1+1/2!*x^2+5/4!*x^4+61/6!*x^6+937/8!*x^8...