Bessel functions of the second kind
GPTKB entity
Statements (35)
| Predicate | Object |
|---|---|
| gptkbp:instance_of |
gptkb:Berserker
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| gptkbp:application |
used in quantum mechanics
used in signal processing used in heat conduction problems used in wave propagation problems |
| gptkbp:asymptotic_behavior |
Y_n(x) ~ sqrt(2/(pi*x)) * cos(x -(n*pi/2) -(pi/4)) as x -> infinity
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| gptkbp:defines |
Solutions to Bessel's differential equation that are finite at infinity for certain values of the order.
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| gptkbp:denoted_by |
Y_n(x)
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| gptkbp:differential_equation |
satisfy Bessel's differential equation
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| gptkbp:graph |
Y_n(x) has a series of oscillations
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| gptkbp:has_property |
are oscillatory functions
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| https://www.w3.org/2000/01/rdf-schema#label |
Bessel functions of the second kind
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| gptkbp:order |
can be of any real or complex order
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| gptkbp:orthogonality |
Y_n(x) are orthogonal over certain intervals
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| gptkbp:recurrence_relation |
Y_n(x) = (2n/x) Y_{n-1}(x) -Y_{n-2}(x)
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| gptkbp:related_to |
gptkb:Bessel_functions_of_the_first_kind
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| gptkbp:relationship |
Y_n(x) = (2/pi) * integral from 0 to pi of (cos(n*t -x*sin(t))) dt
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| gptkbp:series |
Y_n(x) can be expressed as a series for small x
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| gptkbp:special_values |
Y_0(0) is undefined
Y_1(0) is undefined Y_n(0) is undefined for n >= 0 |
| gptkbp:used_in |
solving problems in cylindrical coordinates
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| gptkbp:values |
Y_0(1) ≈ 0.765197686557966
Y_1(1) ≈ 0.440050585744933 Y_10(1) ≈ -0.010000000000000 Y_2(1) ≈ -0.223890779141235 Y_3(1) ≈ -0.197951159161145 Y_4(1) ≈ -0.157963849141202 Y_5(1) ≈ -0.124674737173202 Y_6(1) ≈ -0.096328155162303 Y_7(1) ≈ -0.071464167155052 Y_8(1) ≈ -0.049049155198052 Y_9(1) ≈ -0.028978052080052 |
| gptkbp:bfsParent |
gptkb:Friedrich_Bessel
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| gptkbp:bfsLayer |
4
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