hyp2f1_1b_d_series

jeanspy.hyp2f1_jax.hyp2f1_1b_d_series

jeanspy.hyp2f1_jax.hyp2f1_1b_d_series(b, d, w, *, n_terms)

Fixed-term series for 2F1(1, b; d; w) with w in [0,1).

Implemented via a stable recurrence:

term_0 = 1 term_{n+1} = term_n * (b+n)/(d+n) * w sum = Σ_{n=0}^{N-1} term_n

This is reverse-mode differentiable (static loop bounds).

Notes

Inputs and units. Dimensionless b, d and w; w is in [0,1). The shapes of b and d must broadcast to the shape of w. n_terms is the static term count.

Returns and shape. Approximation to 2F1(1,b;d;w), with the shape of w.

Validity. The denominator d must avoid nonpositive integer poles. The fixed series converges slowly near w=1; check the chosen term count.

Errors. This helper does not validate the input domain; singular parameters or invalid inputs can produce NaN/inf.

Backend. JAX arrays on the configured CPU/GPU, with dtype set before import.

Differentiation. Fixed-loop continuous expressions support autodiff in their valid regions; piecewise thresholds and parameter singularities need checks.

Examples. examples/docs_numerics.py

Parameters:

• b (jax.Array | float)

• d (jax.Array | float)

• w (jax.Array | float)

• n_terms (int)

Return type:

jax.Array