A245308 -id:A245308 - 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)!).

A245119 G.f. satisfies: A(x) = 1 + x^2 + x^2*A'(x)/A(x).

Original entry on oeis.org

1, 0, 1, 2, 6, 22, 100, 554, 3654, 28014, 244572, 2392042, 25877610, 306553246, 3944541224, 54764396346, 815786104186, 12976263731454, 219490418886728, 3933636232278866, 74453982353188846, 1484056255756797222, 31071499784792496588, 681729867750992165514, 15641641334118250802462

Offset: 0

Paul D. Hanna, Jul 24 2014

nonn

			G.f.: A(x) = 1 + x^2 + 2*x^3 + 6*x^4 + 22*x^5 + 100*x^6 + 554*x^7 + 3654*x^8 +...
where the logarithmic derivative equals (A(x) - 1 - x^2)/x^2:
A'(x)/A(x) = 2*x + 6*x^2 + 22*x^3 + 100*x^4 + 554*x^5 + 3654*x^6 +...+ a(n+2)*x^n +...
thus the logarithm begins:
log(A(x)) = 2*x^2/2 + 6*x^3/3 + 22*x^4/4 + 100*x^5/5 + 554*x^6/6 + 3654*x^7/7 +...+ a(n+1)*x^n/n +...

Compare g.f. to: G(x) = 1 + x + x^2*G'(x)/G(x) when G(x) = 1/(1-x).

Paul D. Hanna, Table of n, a(n) for n = 0..300

Cf. A245308.

{a(n)=local(A=1+x^2);for(i=1,n,A = 1 + x^2 + x^2*A'/(A +x*O(x^n)));polcoeff(A,n)}
for(n=0,30,print1(a(n),", "))

/* From A(x) = exp(-x)*G(x), where G(x) = e.g.f. of A245308: */
{a(n)=local(G=1+x);for(i=1,n,G = exp(x +x*O(x^n))*(1 + x^2*G'/(G +x*O(x^n))));
polcoeff(exp(-x +x*O(x^n))*G,n)}
for(n=0,30,print1(a(n),", "))

G.f. A(x) satisfies:
(1) A(x) = exp(-x)*G(x) where G(x) = exp(x)*(1 + x^2*G'(x)/G(x)) is the e.g.f. of A245308.
(2) A(x) = exp( Integral (A(x) - 1 - x^2)/x^2 dx ).
a(n) ~ BesselJ(1,2) * (n-1)!. - Vaclav Kotesovec, Jul 25 2014

cp's OEIS Frontend

A348607 Decimal expansion of BesselJ(1,2).

Views

Author

Keywords

Examples

Crossrefs

Programs

Mathematica

PARI

Sage

Formula

A245119 G.f. satisfies: A(x) = 1 + x^2 + x^2*A'(x)/A(x).

Views

Author

Keywords

Examples

References

Links

Crossrefs

Programs

PARI

PARI

Formula