def _sympysage_ff(self):
"""
EXAMPLES::
sage: from sympy import Symbol, ff
sage: _ = var('x, y')
sage: ffxy = ff(Symbol('x'), Symbol('y'))
sage: assert falling_factorial(x,y)._sympy_() == ffxy.rewrite('gamma') # known bug
sage: assert falling_factorial(x,y) == ffxy._sage_()
"""
from sage.arith.all import falling_factorial
return falling_factorial(self.args[0]._sage_(), self.args[1]._sage_())
def _sympysage_ff(self):
"""
EXAMPLES::
sage: from sympy import Symbol, ff
sage: _ = var('x, y')
sage: ffxy = ff(Symbol('x'), Symbol('y'))
sage: assert falling_factorial(x,y)._sympy_() == ffxy.rewrite('gamma') # known bug
sage: assert falling_factorial(x,y) == ffxy._sage_()
"""
from sage.arith.all import falling_factorial
return falling_factorial(self.args[0]._sage_(), self.args[1]._sage_())
def inverse_gamma_derivative(shift, r):
"""
Return value of `r`-th derivative of 1/Gamma
at alpha-shift.
"""
if r == 0:
result = iga*falling_factorial(alpha-1, shift)
else:
result = limit((1/gamma(s)).diff(s, r), s=alpha-shift)
try:
return coefficient_ring(result)
except TypeError:
return result
def inverse_gamma_derivative(shift, r):
"""
Return value of `r`-th derivative of 1/Gamma
at alpha-shift.
"""
if r == 0:
result = iga * falling_factorial(alpha - 1, shift)
else:
result = limit((1 / gamma(s)).diff(s, r), s=alpha - shift)
try:
return coefficient_ring(result)
except TypeError:
return result
