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Malmstén's Differential Equation

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The ordinary differential equation

y^('')+r/zy^'=(Az^m+s/(z^2))y.
(1)

It has solution

y=c_1I_(-nu)((2sqrt(A)z^(m/2+1))/(m+2))z^((1-r)/2) +c_2I_nu((2sqrt(A)z^(m/2+1))/(m+2))z^((1-r)/2),
(2)

where

nu=(sqrt((r-1)^2+4s))/(m+2)
(3)

and I_nu(z) is a modified Bessel function of the first kind.

See also

Modified Bessel Function of the First Kind

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References

Watson, G. N. A Treatise on the Theory of Bessel Functions, 2nd ed. Cambridge, England: Cambridge University Press, pp. 99-100, 1966.

Referenced on Wolfram|Alpha

Malmstén's Differential Equation

Cite this as:

Weisstein, Eric W. "Malmstén's Differential Equation." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/MalmstensDifferentialEquation.html

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