Spherical bessel differential function.

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The discussion centers on the Spherical Bessel differential equation, specifically its order as stated in various sources. The equation presented is {(d²/dx²)+(d/dx)+[x²-(n+1/2)²]}z = 0. There is a discrepancy regarding the order of the equation, with the original poster believing it to be n+1/2, while other sources claim it is 1/2. This raises questions about the definition of order in mathematical contexts, particularly how it relates to the squared terms in the equation. Clarification on this topic is sought, especially regarding the conflicting information from different references.
mccoy1
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I was looking at the above equation here:
http://mathworld.wolfram.com/SphericalBesselDifferentialEquation.html
Which has the following equation:
{(d ²/dx²)+(d/dx)+[x²-(n+1/2)²] }z =0.
In my opinion, this equation is of the order n+1/2 but the website and books claim it's of the order of a 1/2. How can that be? In maths books the order is what ever is squared and the solutions are of that order.
Thank you.
 
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