A334632 Decimal expansion of Sum_{k>=0} (-1)^k / ((2*k)!)^2.

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

Offset: 0

Author

Vaclav Kotesovec, Sep 10 2020

Keywords

• nonn
• cons

Examples

			0.75173418271380822855099890123074657595958657660729200273884...
		

References

• Jerome Spanier and Keith B. Oldham, "Atlas of Functions", Hemisphere Publishing Corp., 1987, chapter 55, page 552.

Links

• Eric Weisstein's World of Mathematics, Kelvin Functions.
• Wikipedia, Kelvin functions.

Crossrefs

Cf. A334379.

Programs

Maple

evalf(Sum((-1)^k/(2*k)!^2, k=0..infinity), 120);

Mathematica

RealDigits[KelvinBer[0, 2], 10, 120][[1]]
RealDigits[Re[Hypergeometric0F1Regularized[1, I]], 10, 120][[1]]
RealDigits[HypergeometricPFQ[{}, {1/2, 1/2, 1}, -1/16], 10, 120][[1]] (* Vaclav Kotesovec, Jul 19 2021 *)

PARI

sumalt(k=0, (-1)^k/(2*k)!^2)

Formula

Equals Re(BesselJ(0, 2*exp(3*Pi*i/4))).