spherical Bessel function of the first kind
GPTKB entity
Statements (25)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
gptkb:software |
| gptkbp:asymptoticForm |
j_n(x) ~ sin(x - nπ/2)/x for large x
|
| gptkbp:category |
orthogonal polynomials
solutions to differential equations |
| gptkbp:differential |
x^2 y'' + 2x y' + [x^2 - n(n+1)]y = 0
|
| gptkbp:domain |
real numbers
|
| gptkbp:expressedIn |
j_n(x) = sqrt(π/(2x)) J_{n+1/2}(x)
|
| gptkbp:firstFew |
j_2(x) = ( (3/x^3) - (1/x) ) sin(x) - (3 cos(x)/x^2 )
j_0(x) = sin(x)/x j_1(x) = (sin(x)/x^2) - (cos(x)/x) |
| https://www.w3.org/2000/01/rdf-schema#label |
spherical Bessel function of the first kind
|
| gptkbp:namedAfter |
gptkb:Friedrich_Bessel
|
| gptkbp:notation |
j_n(x)
|
| gptkbp:orthogonal |
on [0,∞) with weight x^2
|
| gptkbp:parameter |
order n
argument x |
| gptkbp:recurrence |
j_{n-1}(x) and j_{n+1}(x)
|
| gptkbp:relatedTo |
Bessel function
|
| gptkbp:seriesExpansion |
j_n(x) = x^n / ( (2n+1)!! ) + ...
|
| gptkbp:usedIn |
mathematical physics
quantum mechanics wave equations |
| gptkbp:bfsParent |
gptkb:spherical_Bessel_function
|
| gptkbp:bfsLayer |
7
|