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  "body": "\n## Summary\n\nThe Lommel functions $s_{\\mu,\\nu}$ and $S_{\\mu,\\nu}$ are particular solutions of Bessel's equation with right-hand side $z^{\\mu + 1}$.\nThey contain the [[Struve function|K290RBT8GB]] and the [[Anger function|9P87VQZ0P7]] as special cases, up to adding Bessel functions.\nThey give a common frame for the inhomogeneous Bessel equations met in physics.\n\n## Explanations\n\n### L1 human\n\nBessel's equation with zero right-hand side has the Bessel functions as solutions.\nIf the right-hand side is a power $z^{\\mu+1}$, one needs one extra solution to describe all the others.\nThe Lommel function $s_{\\mu,\\nu}$ is such a solution, written as a power series that starts with $z^{\\mu+1}$.\nFor example, with $\\mu = 1$ and $\\nu = 0$ the constant $1$ already solves the equation, since $z^2 \\cdot 0 + z \\cdot 0 + z^2 \\cdot 1 = z^2$.\nThe Lommel function is the solution that starts with $\\frac{z^2}{4}$, namely $s_{1,0}(z) = 1 - J_0(z)$.\n",
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