A231532 Decimal expansion of the real part of Sum_{n=0..inf}(1/c_n), c_0=1, c_n=c_(n-1)*(n+I).

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

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 real part of expim(1,1). The decimal expansion of the imaginary part is in A231533 and that of the absolute value in A231534.

Examples

			1.59154781473285195733677988...
		

Links

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

Crossrefs

Cf. A231533 (imaginary part), A231534 (absolute value), 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);}
real(Expim(1,1))

Formula

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