def jvp(v,z,n=1):
"""Return the nth derivative of Jv(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 jv(v,z)
else:
return bessel_diff_formula(v, z, n, jv, -1)
def jvp(v,z,n=1):
"""Return the nth derivative of Jv(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 jv(v,z)
else:
return bessel_diff_formula(v, z, n, jv, -1)
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))
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))