A318224 -id:A318224 - cp's OEIS frontend

A348607 Decimal expansion of BesselJ(1,2).

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

Offset: 0

Dumitru Damian, Oct 25 2021

			0.5767248077568733872...

Cf. A010790, A054687, A058798, A058797, A133920, A245308, A296168, A301484, A318224.

Bessel function values: A334380 (J(0,1)), A091681 (J(0,2)), A334383 (J(0,sqrt(2))), this sequence (J(1,2)), A197036 (I(0,1)), A070910 (I(0,2)), A334381 (I(0,sqrt(2))), A096789 (I(1,2)).

RealDigits[BesselJ[1, 2], 10, 100][[1]] (* Amiram Eldar, Oct 25 2021 *)

besselj(1, 2) \\ Michel Marcus, Oct 25 2021

Sage
```
bessel_J(1, 2).n(digits=100)
```

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

A330497 a(n) = n! * Sum_{k=0..n} (-1)^k * binomial(n,k) * n^(n - k) / k!.

Original entry on oeis.org

1, 0, 1, 26, 1089, 70124, 6495985, 821315214, 136115947009, 28651724077976, 7470040450004001, 2363470644596843330, 892244303052345224641, 396227360441775922668036, 204487588996059177697597969, 121370399839482643287189048374

Offset: 0

Ilya Gutkovskiy, Dec 18 2019

nonn

Cf. A009940, A025166, A061711, A277423, A307885, A318224, A319392, A330260.

[Factorial(n)*&+[(-1)^k*Binomial(n,k)*n^(n-k)/Factorial(k):k in [0..n]]:n in [0..15]]; // Marius A. Burtea, Dec 18 2019

Join[{1}, Table[n! Sum[(-1)^k Binomial[n, k] n^(n - k)/k!, {k, 0, n}], {n, 1, 15}]]
Join[{1}, Table[n^n n! LaguerreL[n, 1/n], {n, 1, 15}]]
Table[n! SeriesCoefficient[Exp[-x/(1 - n x)]/(1 - n x), {x, 0, n}], {n, 0, 15}]

a(n) = n! * [x^n] exp(-x/(1 - n*x)) / (1 - n*x).
a(n) = Sum_{k=0..n} (-1)^(n - k) * binomial(n,k)^2 * n^k * k!.
a(n) ~ sqrt(2*Pi) * BesselJ(0,2) * n^(2*n + 1/2) / exp(n). - Vaclav Kotesovec, Dec 18 2019

cp's OEIS Frontend

A348607 Decimal expansion of BesselJ(1,2).

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