This picture shows the mathematics that Planck used to find a solution to the blackbody problem.

If you want to learn more details you may watch the youtube video:

https://youtu.be/FnTNv-4kVbY

If you want to learn more, you may consider enrolling in the following course:

https://www.udemy.com/course/the-mathematical-beauty-that-led-to-quantum-physics/?instructorPreviewMode=guest

or alternatively you can check this one:

https://stemabilities.com/products/1663646

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