A386710 -id:A386710 - cp's OEIS frontend

A386927 Continued fraction of BesselI(2, 2 * sqrt(2)).

1, 1, 6, 54, 3, 2, 4, 3, 1, 140, 1, 5, 1, 1, 2, 4, 1, 1, 8, 3, 9, 87, 12, 2, 1, 2, 1, 5, 1, 14, 1, 1, 2, 2, 8, 11, 2, 2, 2, 2, 1, 3, 3, 1, 15, 1, 5, 1, 1, 1, 2, 8, 7, 4, 5, 1, 4, 1, 8, 7, 5, 1, 2, 1, 11, 4, 14, 2, 1, 1, 9, 5, 2, 2, 6, 1, 3, 24, 2, 3, 1, 4, 2, 7, 2, 14, 2, 3, 1, 13, 1, 1, 1, 2, 3, 2, 1, 6, 2

Offset: 1

Kelvin Voskuijl, Aug 08 2025

			1 + 1/(1 + 1/(6 + 1/(...))) = 1.857517...

Cf. A386710 (decimal expansion).

ContinuedFraction[BesselI[2, 2 Sqrt[2]] , 100]

contfrac(besseli(2, 2*sqrt(2))) \\ Amiram Eldar, Aug 08 2025

A386934 Decimal expansion of BesselI(1, 2sqrt(2))/(sqrt(2)BesselI(2, 2*sqrt(2))).

Original entry on oeis.org

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

Offset: 1

Kelvin Voskuijl, Aug 09 2025

			1.2892652359849177261502470461093801583744352570790...

Kelvin Voskuijl, Table of n, a(n) for n = 1..20000

Cf. A145051 (continued fraction), A363679, A386710.

RealDigits[BesselI[1, 2 Sqrt[2]]/(Sqrt[2] BesselI[2, 2 Sqrt[2]]), 10, 100][[1]]

besseli(1, 2*sqrt(2))/(sqrt(2)*besseli(2, 2*sqrt(2)))

Equals ( Sum_{k >= 0} 2^n/((1 + n)n!^2) )/( Sum_{k >= 1} 2^k/((k-1)!*(k+1)!) ).

Equals A363679/A386710.

cp's OEIS Frontend

A386927 Continued fraction of BesselI(2, 2 * sqrt(2)).

Views

Author

Keywords

Examples

Crossrefs

Programs

Mathematica

PARI

A386934 Decimal expansion of BesselI(1, 2sqrt(2))/(sqrt(2)BesselI(2, 2*sqrt(2))).

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Formula

cp's OEIS Frontend

A386927 Continued fraction of BesselI(2, 2 * sqrt(2)).

Views

Author

Keywords

Examples

Crossrefs

Programs

Mathematica

PARI

A386934 Decimal expansion of BesselI(1, 2*sqrt(2))/(sqrt(2)*BesselI(2, 2*sqrt(2))).

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Formula

A386934 Decimal expansion of BesselI(1, 2sqrt(2))/(sqrt(2)BesselI(2, 2*sqrt(2))).