deal with Hermite’s equation: y′′−2xy′+2αy =0, −∞< x <∞. ...........(11.3.13) Use some form of technology to determine the coefficients in the Legendre expansion of the polynomial p(x)=3x3−1
deal with Hermite’s equation: y′′−2xy′+2αy =0, −∞< x <∞. ...........(11.3.13)
Use some form of technology to determine the coefficients in the Legendre expansion of the polynomial p(x)=3x3−1
note :
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As per the question we are given the nth order Hermit's differential equation as :
y'' - 2xy' + 2ny = 0 , x ∈ (-∞, ∞)
{for better visualisation we've substituted α with n}
Now we have to solve this differential equation and we will use Frobenius series solution method to find the two independent series solutions of the Hermit's equation.
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