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# FNPHI

FNPHI = “phi” - One of the \(\varphi\)-functions \(\varphi_0(x)\), \(\varphi_1(x)\), …, where the index of the \(\varphi\)-function is specified with `FNPhiSetIndex()`.

## Notes

The \(\varphi\)-functions are defined as

\[\begin{split}\begin{align} \varphi_0(x)&=e^x,\\ \varphi_1(x)&=\frac{e^x-1}{x},\\ \varphi_k(x)&=\frac{\varphi_{k-1}(x)-1/(k-1)!}{x}. \end{align}\end{split}\]
The default index is \(k=1\).

## See Also

FN: Mathematical Functions, `FN`, `FNType`, `FNSetType()`, `FNPhiSetIndex()`

## Level

beginner

## Location

src/sys/classes/fn/impls/phi/fnphi.c

Index of all FN routines Table of Contents for all manual pages Index of all manual pages