A231533 -id:A231533 - cp's OEIS frontend

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

Stanislav Sykora, Nov 10 2013

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.

			1.59154781473285195733677988...

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

Cf. A231533 (imaginary part), A231534 (absolute value), and A231530, A231531 (respectively, the real and imaginary parts of the expansion coefficient's denominators).

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))

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

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).

Original entry on oeis.org

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

Stanislav Sykora, Nov 10 2013

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.

			1.8426202983147305389585438...

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

Cf. A231532 (real part), A231533 (imaginary part), and A231530, A231531 (respectively, the real and imaginary parts of the expansion coefficient's denominators)

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))

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

cp's OEIS Frontend

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).

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