|
Search: id:A091912
|
|
|
| A091912 |
|
Numerators of Taylor series for log(tan(x)+1/cos(x)). |
|
+0
2
|
|
| 1, 1, 1, 61, 277, 50521, 41581, 199360981, 228135437, 2404879675441, 14814847529501, 69348874393137901, 238685140977801337, 4087072509293123892361, 454540704683713199807
(list; graph; listen)
|
|
|
OFFSET
|
0,4
|
|
|
COMMENT
|
Absolute values of (reduced) numerators of Taylor series for the Gudermannian function gd(x)= 2*arctan(exp(x))-Pi/2. - Tamas Kalmar-Nagy (integers(AT)kalmarnagy.com), Sep 28 2007
|
|
REFERENCES
|
J. S. Robertson, Gudermann and the Simple Pendulum, The College Mathematics Journal, Vol. 28 (1997), No. 4, pp. 271-276
|
|
LINKS
|
Eric Weisstein's World of Mathematics, Gudermannian
Eric Weisstein's World of Mathematics, Inverse Gudermannian
|
|
FORMULA
|
E.g.f.: sech x or gd x. - Tamas Kalmar-Nagy (integers(AT)kalmarnagy.com), Sep 28 2007
|
|
EXAMPLE
|
log(tan(x)+1/cos(x)) = x + 1/6*x^3 + 1/24*x^5 + 61/5040*x^7 + 277/72576*x^9 + ...
gd(x) = x - 1/6*x^3 + 1/24*x^5 - 61/5040*x^7 + 277/72576*x^9 + ....
|
|
PROGRAM
|
(PARI) a(n)=local(X); if(n<0, 0, X=x+O(x^(2*n+2)); numerator(polcoeff(tan(X)+1/cos(X), 2*n+1)))
|
|
CROSSREFS
|
Cf. A000364, A028296.
Sequence in context: A029815 A142424 A140854 this_sequence A142605 A142133 A142217
Adjacent sequences: A091909 A091910 A091911 this_sequence A091913 A091914 A091915
|
|
KEYWORD
|
nonn,frac,easy
|
|
AUTHOR
|
Michael Somos, Feb 12 2004
|
|
|
Search completed in 0.002 seconds
|
