scipy.special.modfresnelp

scipy.special.modfresnelp(x, out=None) = <wrapped_ufunc 'modfresnelp'>

Modified Fresnel positive integrals.

Parameters:

xarray_like

Function argument

outtuple of ndarray, optional

Optional output arrays for the function results

Returns:

fpscalar or ndarray

Integral F_+(x): integral(exp(1j*t*t), t=x..inf)

kpscalar or ndarray

Integral K_+(x): 1/sqrt(pi)*exp(-1j*(x*x+pi/4))*fp

See also

modfresnelm

Notes

Array API Standard Support

modfresnelp has support for Python Array API Standard compatible backends in addition to NumPy. The following combinations of backend and device (or other capability) are supported.

Library	CPU	GPU
NumPy	✅	n/a
CuPy	n/a	⛔
PyTorch	✅	⛔
JAX	✅	⛔
Dask	⛔	n/a

For the NumPy backend, this function supports all NumPy ufunc keyword arguments. Other backends may support out, but typically none of the other ufunc kwargs. out is typically supported for CuPy and PyTorch, but not currently in cases where SciPy relies on a generic Array API implementation or, for PyTorch on CPU, falls back to the NumPy backend. out is never supported for JAX because JAX arrays are immutable. modfresnelp does not currently support out for the PyTorch backend.

See Support for the array API standard for more information.