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  "body": "\n## Summary\n\nA Whittaker transform is an [[integral transform|YCK709QB06]] on $(0, \\infty)$ whose kernel is built from a [[Whittaker function|7EFDMJSVDP]] $W_{\\kappa, \\mu}$ of the product $xy$.\nSeveral normalizations are in use in the literature.\nThe form recorded here contains the [[Laplace transform|0V49JEZW06]] as the special case $\\kappa = \\mu + 1/2$.\nWhittaker functions are confluent hypergeometric functions, so these transforms belong to the study of transforms with special function kernels.\n\n## Explanations\n\n### L1 human\n\nWhittaker functions are solutions of a second order differential equation that also produces the exponential function, the error function and Laguerre polynomials as special cases.\nA Whittaker transform integrates a function against such a solution instead of against $e^{-xy}$.\nWith two parameters $\\kappa$ and $\\mu$ it gives a family of transforms that bends the Laplace transform in two directions.\nFor one choice of the parameters the kernel becomes exactly $e^{-xy}$, and nothing new happens.\n",
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