Kummer confluent hypergeometric function (mpmath, WMA)
Hypergeometric1F1[a, b, z]Numeric evaluation:
Hypergeometric1F1[1, 2, 3.0]
Plot over a subset of reals:
Plot[Hypergeometric1F1[1, 2, x], {x, -5, 5}]
Plot[{Hypergeometric1F1[1/2, Sqrt[2], x], Hypergeometric1F1[1/2, Sqrt[3], x], Hypergeometric1F1[1/2, Sqrt[5], x]}, {x, -4, 4}]
Plot[{Hypergeometric1F1[Sqrt[3], Sqrt[2], z], -0.01}, {z, -10, -2}]
Plot[{Hypergeometric1F1[Sqrt[2], b, 1], Hypergeometric1F1[Sqrt[5], b, 1], Hypergeometric1F1[Sqrt[7], b, 1]}, {b, -3, 3}]
Compute the elementwise values of an array:
Hypergeometric1F1[1, 1, {{1, 0}, {0, 1}}]
Hypergeometric1F1[1/2, 1, x]
Evaluate using complex arguments:
Hypergeometric1F1[2 + I, 2, 0.5]
Large numbers are supported:
Hypergeometric1F1[3, 4, 10^10]
Hypergeometric1F1 evaluates to simpler functions for certain parameters:
Hypergeometric1F1[1/2, 1, x]
Hypergeometric1F1[2, 1, x]
Hypergeometric1F1[1, 1/2, x]