I was curious, so I grabbed three undergraduate-level physics texts I had nearby.
One explicitly recites the Ultraviolet Catastrophe prompted Planck story, complete with Rayleigh's incomplete formula.
One essentially matches the story in section 2, using the lesser version of Rayleigh's formula, but (just like the story) does not explicitly tie Planck's work to it. (That textbook notes "an act of desperation" is a quote from one of Planck's letters.)
The third one is interesting! It says that "late nineteenth century physicists tried to understand the shape of the blackbody spectrum [...] using their knowledge of thermodynamics and electromagnetic waves. Their efforts ended in failure." This third text never mentions Rayleigh by name and doesn't specifically show "Rayleigh's Lesser Formula", but it does graph that formula vs. the observed blackbody radiation (interestingly, as a function of frequency instead of wavelength).
The text then eventually says that in 1900, Planck used a photon argument "to make a theoretical prediction that is in excellent agreement with the experimental spectrum". It does not explicitly state cause and effect, but it's kinda implied from the structure of the writing.
Reading into the third text a smidge, it feels like the result of wanting to use the Rayleigh/Catastrophe story and yet knowing it wasn't quite true.
One explicitly recites the Ultraviolet Catastrophe prompted Planck story, complete with Rayleigh's incomplete formula.
One essentially matches the story in section 2, using the lesser version of Rayleigh's formula, but (just like the story) does not explicitly tie Planck's work to it. (That textbook notes "an act of desperation" is a quote from one of Planck's letters.)
The third one is interesting! It says that "late nineteenth century physicists tried to understand the shape of the blackbody spectrum [...] using their knowledge of thermodynamics and electromagnetic waves. Their efforts ended in failure." This third text never mentions Rayleigh by name and doesn't specifically show "Rayleigh's Lesser Formula", but it does graph that formula vs. the observed blackbody radiation (interestingly, as a function of frequency instead of wavelength).
The text then eventually says that in 1900, Planck used a photon argument "to make a theoretical prediction that is in excellent agreement with the experimental spectrum". It does not explicitly state cause and effect, but it's kinda implied from the structure of the writing.
Reading into the third text a smidge, it feels like the result of wanting to use the Rayleigh/Catastrophe story and yet knowing it wasn't quite true.