Is it Double Dribble?

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from Hicksports.com:

Double dribble - Formally known as "discontinued dribble"; the dribble ends when the dribbler catches the ball, holds it, or touches it with both hands simultaneously. Once the dribbling has stopped, the player cannot dribble again until after another player has touched the ball. (There is one exception: A player may stop dribbling, take a shot at the basket, and begin dribbling again after gaining the rebound.)

from NCAA Rules:
Art. 1. A player shall not dribble a second time after the player’s first dribble
has ended, unless the player subsequently loses control because of:
a. A try for field goal.
b. A bat by an opponent.
c. A pass or fumble that has then touched or been touched by another
player.


Neither seems to support this as illegal; and the first rule quote specifies it as legal.