Sequences

392,541 sequences

sinh(arctan(x)*arctan(x))=2/2!*x^2-16/4!*x^4+488/6!*x^6-30336/8!*x^8...A012461
sinh(arctan(x)*arctan(x))=2/2!*x^2-16/4!*x^4+488/6!*x^6-30336/8!*x^8...
Arcsinh(arctan(x)^2) = 2/2!*x^2 - 16/4!*x^4 + 248/6!*x^6 - 3456/8!*x^8 + ...A012462
Arcsinh(arctan(x)^2) = 2/2!*x^2 - 16/4!*x^4 + 248/6!*x^6 - 3456/8!*x^8 + ...
tanh(arctan(x)*arctan(x))=2/2!*x^2-16/4!*x^4+128/6!*x^6+9984/8!*x^8...A012463
tanh(arctan(x)*arctan(x))=2/2!*x^2-16/4!*x^4+128/6!*x^6+9984/8!*x^8...
arctanh(arctan(x)*arctan(x))=2/2!*x^2-16/4!*x^4+608/6!*x^6-43776/8!*x^8...A012464
arctanh(arctan(x)*arctan(x))=2/2!*x^2-16/4!*x^4+608/6!*x^6-43776/8!*x^8...
cosh(arctan(x)*arctan(x))=1+12/4!*x^4-480/6!*x^6+31248/8!*x^8...A012465
cosh(arctan(x)*arctan(x))=1+12/4!*x^4-480/6!*x^6+31248/8!*x^8...
E.g.f. sec(arctan(x)^2) (even powers only).A012466
E.g.f. sec(arctan(x)^2) (even powers only).
Expansion of e.g.f. sech(arctan(x)^2), even powers only.A012467
Expansion of e.g.f. sech(arctan(x)^2), even powers only.
Expansion of e.g.f. arcsin(cos(x) * log(x+1)).A012468
Expansion of e.g.f. arcsin(cos(x) * log(x+1)).
Expansion of e.g.f. arctan(cos(x) * log(x+1)).A012469
Expansion of e.g.f. arctan(cos(x) * log(x+1)).
arcsinh(cos(x)*log(x+1))=x-1/2!*x^2-2/3!*x^3+6/4!*x^4+13/5!*x^5...A012470
arcsinh(cos(x)*log(x+1))=x-1/2!*x^2-2/3!*x^3+6/4!*x^4+13/5!*x^5...
Expansion of e.g.f. arctanh(cos(x)*log(x+1)).A012471
Expansion of e.g.f. arctanh(cos(x)*log(x+1)).
Expansion of e.g.f.: sec(cos(x)*log(x+1))=1+1/2!*x^2-3/3!*x^3+4/4!*x^4-40/5!*x^5...A012472
Expansion of e.g.f.: sec(cos(x)*log(x+1))=1+1/2!*x^2-3/3!*x^3+4/4!*x^4-40/5!*x^5...
sech(cos(x)*log(x+1))=1-1/2!*x^2+3/3!*x^3+6/4!*x^4-60/5!*x^5...A012473
sech(cos(x)*log(x+1))=1-1/2!*x^2+3/3!*x^3+6/4!*x^4-60/5!*x^5...
Expansion of arcsin(cos(x)*sin(x)) = x - 3/3!*x^3 - 15/5!*x^5 + 357/7!*x^7 + 22305/9!*x^9...A012474
Expansion of arcsin(cos(x)*sin(x)) = x - 3/3!*x^3 - 15/5!*x^5 + 357/7!*x^7 + 22305/9!*x^9...
arctan(cos(x)*sin(x))=x-6/3!*x^3+120/5!*x^5-7056/7!*x^7+758400/9!*x^9...A012475
arctan(cos(x)*sin(x))=x-6/3!*x^3+120/5!*x^5-7056/7!*x^7+758400/9!*x^9...
arcsinh(cos(x)*sin(x))=x-5/3!*x^3+65/5!*x^5-3005/7!*x^7+278465/9!*x^9...A012476
arcsinh(cos(x)*sin(x))=x-5/3!*x^3+65/5!*x^5-3005/7!*x^7+278465/9!*x^9...
arctanh(cos(x)*sin(x))=x-2/3!*x^3-40/5!*x^5+208/7!*x^7+64640/9!*x^9...A012477
arctanh(cos(x)*sin(x))=x-2/3!*x^3-40/5!*x^5+208/7!*x^7+64640/9!*x^9...
sec(cos(x)*sin(x))=1+1/2!*x^2-11/4!*x^4-83/6!*x^6+10505/8!*x^8...A012478
sec(cos(x)*sin(x))=1+1/2!*x^2-11/4!*x^4-83/6!*x^6+10505/8!*x^8...
sech(cos(x)*sin(x))=1-1/2!*x^2+21/4!*x^4-717/6!*x^6+46025/8!*x^8...A012479
sech(cos(x)*sin(x))=1-1/2!*x^2+21/4!*x^4-717/6!*x^6+46025/8!*x^8...
Expansion of e.g.f.: exp(cos(x)*arcsin(x))=1+x+1/2!*x^2-1/3!*x^3-7/4!*x^4-15/5!*x^5...A012480
Expansion of e.g.f.: exp(cos(x)*arcsin(x))=1+x+1/2!*x^2-1/3!*x^3-7/4!*x^4-15/5!*x^5...
sin(cos(x)*arcsin(x))=x-3/3!*x^3+25/5!*x^5-371/7!*x^7+11985/9!*x^9...A012481
sin(cos(x)*arcsin(x))=x-3/3!*x^3+25/5!*x^5-371/7!*x^7+11985/9!*x^9...
arcsin(cos(x)*arcsin(x))=x-1/3!*x^3-7/5!*x^5+23/7!*x^7+8017/9!*x^9...A012482
arcsin(cos(x)*arcsin(x))=x-1/3!*x^3-7/5!*x^5+23/7!*x^7+8017/9!*x^9...
E.g.f.: tan(cos(x)*arcsin(x))=x-20/5!*x^5-56/7!*x^7+20112/9!*x^9...A012483
E.g.f.: tan(cos(x)*arcsin(x))=x-20/5!*x^5-56/7!*x^7+20112/9!*x^9...
arctan(cos(x)*arcsin(x))=x-4/3!*x^3+68/5!*x^5-3064/7!*x^7+265936/9!*x^9...A012484
arctan(cos(x)*arcsin(x))=x-4/3!*x^3+68/5!*x^5-3064/7!*x^7+265936/9!*x^9...
cos(cos(x)*arcsin(x))=1-1/2!*x^2+9/4!*x^4-105/6!*x^6+1393/8!*x^8...A012485
cos(cos(x)*arcsin(x))=1-1/2!*x^2+9/4!*x^4-105/6!*x^6+1393/8!*x^8...
sinh(cos(x)*arcsin(x))=x-1/3!*x^3-15/5!*x^5+359/7!*x^7+3713/9!*x^9...A012486
sinh(cos(x)*arcsin(x))=x-1/3!*x^3-15/5!*x^5+359/7!*x^7+3713/9!*x^9...
arcsinh(cos(x)*arcsin(x))=x-3/3!*x^3+33/5!*x^5-1155/7!*x^7+91553/9!*x^9...A012487
arcsinh(cos(x)*arcsin(x))=x-3/3!*x^3+33/5!*x^5-1155/7!*x^7+91553/9!*x^9...
tanh(cos(x)*arcsin(x))=x-4/3!*x^3+60/5!*x^5-2056/7!*x^7+127376/9!*x^9...A012488
tanh(cos(x)*arcsin(x))=x-4/3!*x^3+60/5!*x^5-2056/7!*x^7+127376/9!*x^9...
arctanh(cos(x)*arcsin(x))=x-12/5!*x^5-168/7!*x^7+8144/9!*x^9...A012489
arctanh(cos(x)*arcsin(x))=x-12/5!*x^5-168/7!*x^7+8144/9!*x^9...
cosh(cos(x)*arcsin(x))=1+1/2!*x^2-7/4!*x^4+25/6!*x^6+1297/8!*x^8...A012490
cosh(cos(x)*arcsin(x))=1+1/2!*x^2-7/4!*x^4+25/6!*x^6+1297/8!*x^8...
sec(cos(x)*arcsin(x))=1+1/2!*x^2-3/4!*x^4-75/6!*x^6+1337/8!*x^8...A012491
sec(cos(x)*arcsin(x))=1+1/2!*x^2-3/4!*x^4-75/6!*x^6+1337/8!*x^8...
sech(cos(x)*arcsin(x))=1-1/2!*x^2+13/4!*x^4-325/6!*x^6+14873/8!*x^8...A012492
sech(cos(x)*arcsin(x))=1-1/2!*x^2+13/4!*x^4-325/6!*x^6+14873/8!*x^8...
Take every 5th term of Padovan sequence A000931, beginning with the fifth term.A012493
Take every 5th term of Padovan sequence A000931, beginning with the fifth term.
Expansion of e.g.f. arctan(sin(x)) (odd powers only).A012494
Expansion of e.g.f. arctan(sin(x)) (odd powers only).
Expansion of e.g.f. arcsinh(sin(x)) (odd powers only).A012495
Expansion of e.g.f. arcsinh(sin(x)) (odd powers only).
exp(cos(x)*arctan(x))=1+x+1/2!*x^2-4/3!*x^3-19/4!*x^4+445/6!*x^6...A012496
exp(cos(x)*arctan(x))=1+x+1/2!*x^2-4/3!*x^3-19/4!*x^4+445/6!*x^6...
sin(cos(x)*arctan(x))=x-6/3!*x^3+100/5!*x^5-4256/7!*x^7+302352/9!*x^9...A012497
sin(cos(x)*arctan(x))=x-6/3!*x^3+100/5!*x^5-4256/7!*x^7+302352/9!*x^9...
arcsin(cos(x)*arctan(x))=x-4/3!*x^3+8/5!*x^5+128/7!*x^7+25216/9!*x^9...A012498
arcsin(cos(x)*arctan(x))=x-4/3!*x^3+8/5!*x^5+128/7!*x^7+25216/9!*x^9...
Expansion of e.g.f. tan(cos(x)*arctan(x)) (odd powers only).A012499
Expansion of e.g.f. tan(cos(x)*arctan(x)) (odd powers only).
arctan(cos(x)*arctan(x))=x-7/3!*x^3+173/5!*x^5-11779/7!*x^7...A012500
arctan(cos(x)*arctan(x))=x-7/3!*x^3+173/5!*x^5-11779/7!*x^7...
cos(cos(x)*arctan(x))=1-1/2!*x^2+21/4!*x^4-645/6!*x^6+34153/8!*x^8...A012501
cos(cos(x)*arctan(x))=1-1/2!*x^2+21/4!*x^4-645/6!*x^6+34153/8!*x^8...
sinh(cos(x)*arctan(x))=x-4/3!*x^3+1304/7!*x^7-109120/9!*x^9...A012502
sinh(cos(x)*arctan(x))=x-4/3!*x^3+1304/7!*x^7-109120/9!*x^9...
arcsinh(cos(x)*arctan(x))=x-6/3!*x^3+108/5!*x^5-5880/7!*x^7...A012503
arcsinh(cos(x)*arctan(x))=x-6/3!*x^3+108/5!*x^5-5880/7!*x^7...
tanh(cos(x)*arctan(x))=x-7/3!*x^3+165/5!*x^5-9931/7!*x^7...A012504
tanh(cos(x)*arctan(x))=x-7/3!*x^3+165/5!*x^5-9931/7!*x^7...
arctanh(cos(x)*arctan(x))=x-3/3!*x^3-27/5!*x^5+777/7!*x^7+48905/9!*x^9...A012505
arctanh(cos(x)*arctan(x))=x-3/3!*x^3-27/5!*x^5+777/7!*x^7+48905/9!*x^9...
cosh(cos(x)*arctan(x))=1+1/2!*x^2-19/4!*x^4+445/6!*x^6-14663/8!*x^8...A012506
cosh(cos(x)*arctan(x))=1+1/2!*x^2-19/4!*x^4+445/6!*x^6-14663/8!*x^8...
sec(cos(x)*arctan(x))=1+1/2!*x^2-15/4!*x^4+105/6!*x^6+8897/8!*x^8...A012507
sec(cos(x)*arctan(x))=1+1/2!*x^2-15/4!*x^4+105/6!*x^6+8897/8!*x^8...
sech(cos(x)*arctan(x))=1-1/2!*x^2+25/4!*x^4-1105/6!*x^6+91313/8!*x^8...A012508
sech(cos(x)*arctan(x))=1-1/2!*x^2+25/4!*x^4-1105/6!*x^6+91313/8!*x^8...
E.g.f.: -log(cos(x)*cos(x)) (even powers only).A012509
E.g.f.: -log(cos(x)*cos(x)) (even powers only).
Expansion of e.g.f.: sin(sinh(x)*log(x+1))=2/2!*x^2-3/3!*x^3+12/4!*x^4-40/5!*x^5...A012510
Expansion of e.g.f.: sin(sinh(x)*log(x+1))=2/2!*x^2-3/3!*x^3+12/4!*x^4-40/5!*x^5...