Sequences

392,541 sequences

Expansion of e.g.f. arcsin(arctanh(x) * exp(x)).A012711
Expansion of e.g.f. arcsin(arctanh(x) * exp(x)).
E.g.f.: tan(arctanh(x)*exp(x)).A012712
E.g.f.: tan(arctanh(x)*exp(x)).
E.g.f.: arctan(arctanh(x)*exp(x))=x+2/2!*x^2+3/3!*x^3-12/4!*x^4-147/5!*x^5...A012713
E.g.f.: arctan(arctanh(x)*exp(x))=x+2/2!*x^2+3/3!*x^3-12/4!*x^4-147/5!*x^5...
E.g.f.: cos(arctanh(x)*exp(x))=1-1/2!*x^2-6/3!*x^3-31/4!*x^4-140/5!*x^5...A012714
E.g.f.: cos(arctanh(x)*exp(x))=1-1/2!*x^2-6/3!*x^3-31/4!*x^4-140/5!*x^5...
Expansion of e.g.f. sinh(arctanh(x) * exp(x)).A012715
Expansion of e.g.f. sinh(arctanh(x) * exp(x)).
arcsinh(arctanh(x)*exp(x))=x+2/2!*x^2+4/3!*x^3-52/5!*x^5-440/6!*x^6...A012716
arcsinh(arctanh(x)*exp(x))=x+2/2!*x^2+4/3!*x^3-52/5!*x^5-440/6!*x^6...
arctanh(arctanh(x)*exp(x))=x+2/2!*x^2+7/3!*x^3+36/4!*x^4+293/5!*x^5...A012717
arctanh(arctanh(x)*exp(x))=x+2/2!*x^2+7/3!*x^3+36/4!*x^4+293/5!*x^5...
cosh(arctanh(x)*exp(x))=1+1/2!*x^2+6/3!*x^3+33/4!*x^4+180/5!*x^5...A012718
cosh(arctanh(x)*exp(x))=1+1/2!*x^2+6/3!*x^3+33/4!*x^4+180/5!*x^5...
sec(arctanh(x)*exp(x))=1+1/2!*x^2+6/3!*x^3+37/4!*x^4+260/5!*x^5...A012719
sec(arctanh(x)*exp(x))=1+1/2!*x^2+6/3!*x^3+37/4!*x^4+260/5!*x^5...
sech(arctanh(x)*exp(x))=1-1/2!*x^2-6/3!*x^3-27/4!*x^4-60/5!*x^5...A012720
sech(arctanh(x)*exp(x))=1-1/2!*x^2-6/3!*x^3-27/4!*x^4-60/5!*x^5...
exp(arctanh(x)*sin(x))=1+2/2!*x^2+16/4!*x^4+350/6!*x^6+16280/8!*x^8...A012721
exp(arctanh(x)*sin(x))=1+2/2!*x^2+16/4!*x^4+350/6!*x^6+16280/8!*x^8...
arcsinh(arctanh(x)*sin(x))=2/2!*x^2+4/4!*x^4-10/6!*x^6+1160/8!*x^8...A012722
arcsinh(arctanh(x)*sin(x))=2/2!*x^2+4/4!*x^4-10/6!*x^6+1160/8!*x^8...
exp(arctanh(x)*arcsin(x))=1+2/2!*x^2+24/4!*x^4+718/6!*x^6+40040/8!*x^8...A012723
exp(arctanh(x)*arcsin(x))=1+2/2!*x^2+24/4!*x^4+718/6!*x^6+40040/8!*x^8...
sinh(arctanh(x)*arcsin(x))=2/2!*x^2+12/4!*x^4+358/6!*x^6+19992/8!*x^8...A012724
sinh(arctanh(x)*arcsin(x))=2/2!*x^2+12/4!*x^4+358/6!*x^6+19992/8!*x^8...
Expansion of e.g.f. exp(arctanh(x)*tan(x)) (even powers only).A012725
Expansion of e.g.f. exp(arctanh(x)*tan(x)) (even powers only).
arctanh(arctanh(x)*tan(x))=2/2!*x^2+16/4!*x^4+560/6!*x^6+39296/8!*x^8...A012726
arctanh(arctanh(x)*tan(x))=2/2!*x^2+16/4!*x^4+560/6!*x^6+39296/8!*x^8...
exp(arctanh(x)*arctan(x))=1+2/2!*x^2+12/4!*x^4+328/6!*x^6+13328/8!*x^8...A012727
exp(arctanh(x)*arctan(x))=1+2/2!*x^2+12/4!*x^4+328/6!*x^6+13328/8!*x^8...
sin(arctanh(x)*arctan(x))=2/2!*x^2+88/6!*x^6+112032/10!*x^10...A012728
sin(arctanh(x)*arctan(x))=2/2!*x^2+88/6!*x^6+112032/10!*x^10...
arcsin(arctanh(x)*arctan(x))=2/2!*x^2+328/6!*x^6+1402272/10!*x^10...A012729
arcsin(arctanh(x)*arctan(x))=2/2!*x^2+328/6!*x^6+1402272/10!*x^10...
tan(arctanh(x)*arctan(x))=2/2!*x^2+448/6!*x^6+2138112/10!*x^10...A012730
tan(arctanh(x)*arctan(x))=2/2!*x^2+448/6!*x^6+2138112/10!*x^10...
arctan(arctanh(x)*arctan(x))=2/2!*x^2-32/6!*x^6+283392/10!*x^10...A012731
arctan(arctanh(x)*arctan(x))=2/2!*x^2-32/6!*x^6+283392/10!*x^10...
cos(arctanh(x)*arctan(x)) = 1-12/4!*x^4-9968/8!*x^8-77575872/12!*x^12...A012732
cos(arctanh(x)*arctan(x)) = 1-12/4!*x^4-9968/8!*x^8-77575872/12!*x^12...
arcsinh(arctanh(x)*arctan(x))=2/2!*x^2+88/6!*x^6+353952/10!*x^10...A012733
arcsinh(arctanh(x)*arctan(x))=2/2!*x^2+88/6!*x^6+353952/10!*x^10...
arctanh(arctanh(x)*arctan(x))=2/2!*x^2+448/6!*x^6+2380032/10!*x^10...A012734
arctanh(arctanh(x)*arctan(x))=2/2!*x^2+448/6!*x^6+2380032/10!*x^10...
cosh(arctanh(x)*arctan(x)) = 1+12/4!*x^4+13328/8!*x^8+123701952/12!*x^12...A012735
cosh(arctanh(x)*arctan(x)) = 1+12/4!*x^4+13328/8!*x^8+123701952/12!*x^12...
sec(arctanh(x)*arctan(x)) = 1+12/4!*x^4+20048/8!*x^8+255870912/12!*x^12...A012736
sec(arctanh(x)*arctan(x)) = 1+12/4!*x^4+20048/8!*x^8+255870912/12!*x^12...
sech(arctanh(x)*arctan(x))=1-12/4!*x^4-3248/8!*x^8-25240512/12!*x^12...A012737
sech(arctanh(x)*arctan(x))=1-12/4!*x^4-3248/8!*x^8-25240512/12!*x^12...
exp(arctanh(x)*cos(x)) = 1+x+1/2!*x^2-3/4!*x^4+45/6!*x^6+504/7!*x^7...A012738
exp(arctanh(x)*cos(x)) = 1+x+1/2!*x^2-3/4!*x^4+45/6!*x^6+504/7!*x^7...
sin(arctanh(x)*cos(x))=x-2/3!*x^3+20/5!*x^5-16/7!*x^7+14096/9!*x^9...A012739
sin(arctanh(x)*cos(x))=x-2/3!*x^3+20/5!*x^5-16/7!*x^7+14096/9!*x^9...
arcsin(arctanh(x)*cos(x))=x+8/5!*x^5+448/7!*x^7+32384/9!*x^9...A012740
arcsin(arctanh(x)*cos(x))=x+8/5!*x^5+448/7!*x^7+32384/9!*x^9...
tan(arctanh(x)*cos(x))=x+1/3!*x^3+5/5!*x^5+509/7!*x^7+44393/9!*x^9...A012741
tan(arctanh(x)*cos(x))=x+1/3!*x^3+5/5!*x^5+509/7!*x^7+44393/9!*x^9...
Expansion of e.g.f. arctan(arctanh(x)*cos(x)) (odd powers only).A012742
Expansion of e.g.f. arctan(arctanh(x)*cos(x)) (odd powers only).
cos(arctanh(x)*cos(x))=1-1/2!*x^2+5/4!*x^4-85/6!*x^6-887/8!*x^8...A012743
cos(arctanh(x)*cos(x))=1-1/2!*x^2+5/4!*x^4-85/6!*x^6-887/8!*x^8...
sinh(arctanh(x)*cos(x))=x+504/7!*x^7+24384/9!*x^9+2375296/11!*x^11...A012744
sinh(arctanh(x)*cos(x))=x+504/7!*x^7+24384/9!*x^9+2375296/11!*x^11...
arcsinh(arctanh(x)*cos(x))=x-2/3!*x^3+28/5!*x^5-520/7!*x^7+59728/9!*x^9...A012745
arcsinh(arctanh(x)*cos(x))=x-2/3!*x^3+28/5!*x^5-520/7!*x^7+59728/9!*x^9...
arctanh(arctanh(x)*cos(x)) = x+1/3!*x^3+13/5!*x^5+677/7!*x^7+54937/9!*x^9...A012746
arctanh(arctanh(x)*cos(x)) = x+1/3!*x^3+13/5!*x^5+677/7!*x^7+54937/9!*x^9...
cosh(arctanh(x)*cos(x))=1+1/2!*x^2-3/4!*x^4+45/6!*x^6+2457/8!*x^8...A012747
cosh(arctanh(x)*cos(x))=1+1/2!*x^2-3/4!*x^4+45/6!*x^6+2457/8!*x^8...
Expansion of e.g.f. sec(arctanh(x)*cos(x)), only even powers.A012748
Expansion of e.g.f. sec(arctanh(x)*cos(x)), only even powers.
sech(arctanh(x)*cos(x))=1-1/2!*x^2+9/4!*x^4-225/6!*x^6+6993/8!*x^8...A012749
sech(arctanh(x)*cos(x))=1-1/2!*x^2+9/4!*x^4-225/6!*x^6+6993/8!*x^8...
exp(arctanh(x)*sinh(x)) = 1+2/2!*x^2+24/4!*x^4+670/6!*x^6+34664/8!*x^8...A012750
exp(arctanh(x)*sinh(x)) = 1+2/2!*x^2+24/4!*x^4+670/6!*x^6+34664/8!*x^8...
tan(arctanh(x)*sinh(x))=2/2!*x^2+12/4!*x^4+430/6!*x^6+27384/8!*x^8...A012751
tan(arctanh(x)*sinh(x))=2/2!*x^2+12/4!*x^4+430/6!*x^6+27384/8!*x^8...
exp(arctanh(x)*arcsinh(x)) = 1+2/2!*x^2+16/4!*x^4+398/6!*x^6+18072/8!*x^8...A012752
exp(arctanh(x)*arcsinh(x)) = 1+2/2!*x^2+16/4!*x^4+398/6!*x^6+18072/8!*x^8...
tan(arctanh(x)*arcsinh(x))=2/2!*x^2+4/4!*x^4+398/6!*x^6+10344/8!*x^8...A012753
tan(arctanh(x)*arcsinh(x))=2/2!*x^2+4/4!*x^4+398/6!*x^6+10344/8!*x^8...
exp(arctanh(x)*tanh(x)) = 1+2/2!*x^2+12/4!*x^4+280/6!*x^6+13328/8!*x^8...A012754
exp(arctanh(x)*tanh(x)) = 1+2/2!*x^2+12/4!*x^4+280/6!*x^6+13328/8!*x^8...
tan(arctanh(x)*tanh(x))=2/2!*x^2+400/6!*x^6+2688/8!*x^8...A012755
tan(arctanh(x)*tanh(x))=2/2!*x^2+400/6!*x^6+2688/8!*x^8...
exp(arctanh(x)*arctanh(x))=1+2/2!*x^2+28/4!*x^4+968/6!*x^6+61584/8!*x^8...A012756
exp(arctanh(x)*arctanh(x))=1+2/2!*x^2+28/4!*x^4+968/6!*x^6+61584/8!*x^8...
tan(arctanh(x)^2) = 2/2!*x^2 + 16/4!*x^4 + 608/6!*x^6 + 43776/8!*x^8 + ...A012757
tan(arctanh(x)^2) = 2/2!*x^2 + 16/4!*x^4 + 608/6!*x^6 + 43776/8!*x^8 + ...
Expansion of e.g.f. arcsin(cosh(x) * log(x+1)).A012758
Expansion of e.g.f. arcsin(cosh(x) * log(x+1)).
Expansion of e.g.f.: arctan(cosh(x)*log(x+1))=x-1/2!*x^2+3/3!*x^3-57/5!*x^5+405/6!*x^6...A012759
Expansion of e.g.f.: arctan(cosh(x)*log(x+1))=x-1/2!*x^2+3/3!*x^3-57/5!*x^5+405/6!*x^6...
Expansion of e.g.f. arcsinh(cosh(x) * log(x+1)).A012760
Expansion of e.g.f. arcsinh(cosh(x) * log(x+1)).