Exemplo n.º 1
0
def hyp0f1(v,z):
    """Confluent hypergeometric limit function 0F1.
    Limit as q->infinity of 1F1(q;a;z/q)
    """
    z = asarray(z)
    if issubdtype(z.dtype, complexfloating):
        arg = 2*sqrt(abs(z))
        num = where(z>=0, iv(v-1,arg), jv(v-1,arg))
        den = abs(z)**((v-1.0)/2)
    else:
        num = iv(v-1,2*sqrt(z))
        den = z**((v-1.0)/2.0)
    num *= gamma(v)
    return where(z==0,1.0,num/ asarray(den))
Exemplo n.º 2
0
def hyp0f1(v, z):
    r"""Confluent hypergeometric limit function 0F1.

    Parameters
    ----------
    v, z : array_like
        Input values.

    Returns
    -------
    hyp0f1 : ndarray
        The confluent hypergeometric limit function.

    Notes
    -----
    This function is defined as:

    .. math:: _0F_1(v,z) = \sum_{k=0}^{\inf}\frac{z^k}{(v)_k k!}.

    It's also the limit as q -> infinity of ``1F1(q;v;z/q)``, and satisfies
    the differential equation :math:``f''(z) + vf'(z) = f(z)`.
    """
    v = atleast_1d(v)
    z = atleast_1d(z)
    v, z = np.broadcast_arrays(v, z)
    arg = 2 * sqrt(abs(z))
    old_err = np.seterr(all='ignore')  # for z=0, a<1 and num=inf, next lines
    num = where(z.real >= 0, iv(v - 1, arg), jv(v - 1, arg))
    den = abs(z)**((v - 1.0) / 2)
    num *= gamma(v)
    np.seterr(**old_err)
    num[z == 0] = 1
    den[z == 0] = 1
    return num / den
Exemplo n.º 3
0
def hyp0f1(v, z):
    r"""Confluent hypergeometric limit function 0F1.

    Parameters
    ----------
    v, z : array_like
        Input values.

    Returns
    -------
    hyp0f1 : ndarray
        The confluent hypergeometric limit function.

    Notes
    -----
    This function is defined as:

    .. math:: _0F_1(v,z) = \sum_{k=0}^{\inf}\frac{z^k}{(v)_k k!}.

    It's also the limit as q -> infinity of ``1F1(q;v;z/q)``, and satisfies
    the differential equation :math:``f''(z) + vf'(z) = f(z)`.
    """
    v = atleast_1d(v)
    z = atleast_1d(z)
    v, z = np.broadcast_arrays(v, z)
    arg = 2 * sqrt(abs(z))
    old_err = np.seterr(all='ignore')  # for z=0, a<1 and num=inf, next lines
    num = where(z.real >= 0, iv(v - 1, arg), jv(v - 1, arg))
    den = abs(z)**((v - 1.0) / 2)
    num *= gamma(v)
    np.seterr(**old_err)
    num[z == 0] = 1
    den[z == 0] = 1
    return num / den
Exemplo n.º 4
0
def ivp(v,z,n=1):
    """Return the nth derivative of Iv(z) with respect to z.
    """
    if not isinstance(n,types.IntType) or (n<0):
        raise ValueError("n must be a non-negative integer.")
    if n == 0:
        return iv(v,z)
    else:
        return bessel_diff_formula(v, z, n, iv, 1)
Exemplo n.º 5
0
def ivp(v, z, n=1):
    """Return the nth derivative of Iv(z) with respect to z.
    """
    if not isinstance(n, types.IntType) or (n < 0):
        raise ValueError("n must be a non-negative integer.")
    if n == 0:
        return iv(v, z)
    else:
        return bessel_diff_formula(v, z, n, iv, 1)