A231533 Decimal expansion of the negative imaginary part of Sum_{n=0..inf}(1/c_n), c_0=1, c_n=c_(n-1)*(n+I).

9, 2, 8, 5, 6, 0, 7, 7, 7, 3, 2, 1, 8, 4, 5, 5, 8, 6, 6, 6, 7, 2, 0, 2, 9, 3, 2, 8, 5, 6, 6, 9, 8, 7, 2, 0, 2, 8, 9, 8, 6, 9, 7, 4, 6, 3, 3, 1, 5, 6, 5, 6, 5, 9, 9, 9, 2, 3, 1, 4, 8, 3, 3, 9, 0, 9, 9, 5, 0, 0, 6, 1, 7, 0, 2, 6, 0, 3, 6, 5, 9, 7, 6, 7, 1, 9, 0, 7, 4, 5, 8, 4, 5, 5, 1, 2, 2, 7, 1, 8, 1, 0, 0, 7, 1

Offset: 0

Author

Stanislav Sykora, Nov 10 2013

Keywords

• nonn
• cons

Comments

Consider an extension of exp(x) to an intriguing function, expim(x,y), defined by the power series Sum_{n=0..inf}(x^n/c_n), where c_0 = 1, c_n = c_(n-1)*(n+y*I), so that exp(x) = expim(x,0). The current sequence regards the negative imaginary part of the complex expim(1,1). The decimal expansion of the real part is in A231532 and that of the absolute value in A231534.

Examples

			-0.92856077732184558666720293...
		

Links

• Stanislav Sykora, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A231532, A231534, and A231530, A231531 (respectively the real and imaginary parts of the expansion coefficient's denominators).

Programs

PARI

Expim(x,y)={local (c,k,lastval,val);c = 1.0+0.0*I;lastval = c;k = 1; while (k,c*=x/(k + y*I);val = lastval + c;if (val==lastval, break);   lastval = val;k += 1;);return (val);}
imag(Expim(1,1))

Formula

imag(Sum_{n=0..inf}(1/(A231530(n)+A231531(n)*I))).