A231534 Decimal expansion of the absolute value of Sum_{n=0..inf}(1/c_n), c_0=1, c_n=c_(n-1)*(n+I).

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

Offset: 1

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 absolute value of expim(1,1). The decimal expansions of the real and imaginary parts of expim(1,1) are in A231532 and A231533, respectively.

Examples

			1.8426202983147305389585438...
		

Links

• Stanislav Sykora, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A231532 (real part), A231533 (imaginary part), 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); }
abs(Expim(1, 1))

Formula

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