Zeros of first order spherical bessel function
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heya
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For n=−1,0n=−1,0, finding the roots of the spherical Bessel functions jn(x)jn(x) and yn(x)yn(x) is somewhat easy, since:
j−1(x)j0(x)==cosxxsinc(x)y−1(x)y0(x)==sinc(x)−cosxxj−1(x)=cosxxy−1(x)=sinc(x)j0(x)=sinc(x)y0(x)=−cosxx
where sinc(x)=sinxxsinc(x)=sinxx is the sine cardinal. Solving for zeros of other orders results in rather complicated transcendental equations, which I doubt have closed-form solutions. However, you will want to see these DLMF entries for some more information that can help you in numerically determining the zeros (e.g., asymptotic expansions); approximations derived from formulae there can then be subsequently polished with Newton-Raphson or some other iterative method of choice.
thanls
here is ur answer hope it will help u
plzz mark it as brainliest and follow me
For n=−1,0n=−1,0, finding the roots of the spherical Bessel functions jn(x)jn(x) and yn(x)yn(x) is somewhat easy, since:
j−1(x)j0(x)==cosxxsinc(x)y−1(x)y0(x)==sinc(x)−cosxxj−1(x)=cosxxy−1(x)=sinc(x)j0(x)=sinc(x)y0(x)=−cosxx
where sinc(x)=sinxxsinc(x)=sinxx is the sine cardinal. Solving for zeros of other orders results in rather complicated transcendental equations, which I doubt have closed-form solutions. However, you will want to see these DLMF entries for some more information that can help you in numerically determining the zeros (e.g., asymptotic expansions); approximations derived from formulae there can then be subsequently polished with Newton-Raphson or some other iterative method of choice.
thanls
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