Repository: scipy/scipy
File: scipy/special/_special_ufuncs_docs.cpp (C++)

Code before:
    where :math:`K_v` is the modified Bessel function of the second kind.
    For negative orders, the relation

    .. math:: H^{(1)}_{-v}(z) = H^{(1)}_v(z) \exp(\imath\pi v)

    is used.

    References
    ----------
    .. [1] Donald E. Amos, "AMOS, A Portable Package for Bessel Functions
           of a Complex Argument and Nonnegative Order",
           http://netlib.org/amos/

    Examples
    --------
    For the inhomogenous Helmholtz equation in :math:`\mathbb{R}^2` subject to radiation
    boundary conditions, the Green's function is given by

    .. math::

        G(\mathbf{x}, \mathbf{x}^\prime) =
        \frac{1}{4i} H^{(1)}_0(k|\mathbf{x} - \mathbf{x^\prime}|)

    where :math:`k` is the wavenumber and :math:`H^{(1)}_0` is the Hankel function
    of the first kind and of order zero. In the following example, we will solve the
    Helmholtz equation with two dirac sources.

    >>> import numpy as np
    >>> import matplotlib.pyplot as plt
    >>> from scipy.special import hankel1
    >>> k = 10  # Wavenumber
    >>> sources = [0.5, -0.5]  # Location of two point sources
    >>> x, y = np.linspace(-3, 3, 300), np.linspace(-3, 3, 300)
    >>> Z = np.add.outer(1j*y, x)
    >>> U = np.zeros_like(Z)
    >>> for sz in sources:
    >>>     r = np.abs(Z - sz)
    >>>     U += (1j/4)*hankel1(0, k*r)

    Finally, we will plot the real part of the solution.

    >>> fig, ax = plt.subplots()
    >>> ax.pcolormesh(np.real(Z), np.imag(Z), np.real(U))
    >>> plt.show()
    )";

const char *hankel1e_doc = R"(
    hankel1e(v, z, out=None)

    Exponentially scaled Hankel function of the first kind


Review comment (suggestion):
```suggestion
    Helmholtz equation with two Dirac sources.
```

Code after:
    For negative orders, the relation

    .. math:: H^{(1)}_{-v}(z) = H^{(1)}_v(z) \exp(\imath\pi v)

    is used.

    References
    ----------
    .. [1] Donald E. Amos, "AMOS, A Portable Package for Bessel Functions
           of a Complex Argument and Nonnegative Order",
           http://netlib.org/amos/

    Examples
    --------
    For the inhomogenous Helmholtz equation in :math:`\mathbb{R}^2` subject to radiation
    boundary conditions, the Green's function is given by

    .. math::

        G(\mathbf{x}, \mathbf{x}^\prime) =
        \frac{1}{4i} H^{(1)}_0(k|\mathbf{x} - \mathbf{x^\prime}|)

    where :math:`k` is the wavenumber and :math:`H^{(1)}_0` is the Hankel function
    of the first kind and of order zero. In the following example, we will solve the
    Helmholtz equation with two Dirac sources.

    >>> import numpy as np
    >>> import matplotlib.pyplot as plt
    >>> from scipy.special import hankel1
    >>> k = 10  # Wavenumber
    >>> sources = [0.5, -0.5]  # Location of two point sources
    >>> x, y = np.linspace(-3, 3, 300), np.linspace(-3, 3, 300)
    >>> Z = np.add.outer(1j*y, x)
    >>> U = np.zeros_like(Z)
    >>> for sz in sources:
    ...     r = np.abs(Z - sz)
    ...     U += (1j/4)*hankel1(0, k*r)

    Finally, we will plot the real part of the solution.

    >>> fig, ax = plt.subplots()
    >>> ax.pcolormesh(np.real(Z), np.imag(Z), np.real(U))
    >>> plt.show()
    )";

const char *hankel1e_doc = R"(
    hankel1e(v, z, out=None)

    Exponentially scaled Hankel function of the first kind

    Defined as::