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base/src/functions/engineering/transcendental/README.md
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base/src/functions/engineering/transcendental/README.md
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# Creating tests from transcendental functions
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Excel supports a number of transcendental functions like the error functions, gamma nad beta functions.
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In this folder we have tests for the Bessel functions.
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Some other platform's implementations of those functions are remarkably poor (including Excel), sometimes failing on the third decimal digit. We strive to do better.
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To properly test you need to compute some known values with established arbitrary precision arithmetic.
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I use for this purpose Arb[1], created by the unrivalled Fredrik Johansson[2]. You might find some python bindings, but I use Julia's Nemo[3]:
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```julia
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julia> using Nemo
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julia> CC = AcbField(200)
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julia> besseli(CC("17"), CC("5.6"))
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```
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If you are new to Julia, just install Julia and in the Julia terminal run:
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```
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julia> using Pkg; Pkg.add("Nemo")
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```
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You only need to do that once (like the R philosophy)
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Will give you any Bessel function of any order (integer or not) of any value real or complex
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[1]: https://arblib.org/
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[2]: https://fredrikj.net/
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[3]: https://nemocas.github.io/Nemo.jl/latest/
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