pymiediff.special.pi_tau

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pymiediff.special.pi_tau#

pymiediff.special.pi_tau(n: int, mu: Tensor, **kwargs)#

angular functions tau and pi up to order n

calculated by recurrence relation. Returns all orders up to n, add a new “order” dimension (first dim) to the results

Uses recurrence:

pi_0 = 0, pi_1 = 1 pi_{n+1} = ((2n+1)*mu*pi_n - (n+1)*pi_{n-1}) / n tau_n = n*mu*pi_n - (n+1)*pi_{n-1}

Parameters:

  • n (torch.Tensor or int) – order, use max(n) if a tensor.

  • mu (torch.Tensor) – cosine of the angle

Returns:

tuple (pi, tau).

Return type:

turple

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