A385962 Decimal expansion of the absolute value of the coefficient [x^4] Gamma(x).

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

Offset: 0

Author

R. J. Mathar, Jul 13 2025

Keywords

• nonn
• cons

Comments

The Laurent series Gamma(x) = 1/x + Sum_{i>=0} a_i x^i starts with a_0 = -gamma = -A001620, a_1 = A090998 . a_4 = -0.98199506.. , absolute value here.

Examples

			0.9819950689031452021047014137..
		

Links

• I. S. Gradsteyn, I. M. Ryzhik, Tables of Series and Products, Academic Press (2014) 8.321.1 gives recurrence.

Crossrefs

Cf. A090998 [x^1], A385960 [x^2], A385961 [x^3].

Programs

Maple

(gamma^5 +10*gamma^3*Zeta(2) +20*gamma^2*Zeta(3) +15*(Zeta(2)^2+2*Zeta(4))*gamma +20*Zeta(2)*Zeta(3) +24*Zeta(5))/120 ; evalf(%) ;

Formula

Equals (gamma^5 +10*gamma^3*zeta(2) +20*gamma^2*zeta(3) +15*(zeta(2)^2+2*zeta(4))*gamma +20*zeta(2)*zeta(3) +24*zeta(5))/120 , gamma = A001620, zeta(2) = A013661, zeta(3)=A002117, zeta(4) = A013662, zeta(5) = A013663.