The practice among Sepharadim is to recite the Beracha of "Boreh Peri Ha’adama" on mashed potatoes. Even though mashed potatoes do not resemble a potato, nevertheless, they require the Beracha of "Ha’adama" because they have the same taste as an ordinary potato. This applies as well to "eddge" (potato pancakes), which is prepared by frying grated potato, as well as French fries and potato chips, which are fried slices of potato. Although these products do not have the form or appearance of a potato, they nevertheless require the Beracha of "Ha’adama" because they taste like potato.
The more complex question relates to Pringles, which are prepared from potato flour, and not from actual pieces of potato. Some Halachic authorities maintain that even Pringles require the Beracha of "Ha’adama," because they have the taste of potato. However, the Yalkut Yosef (Berachot, vol. 3, p. 42) notes that a Pringles chip is comprised of only 42 percent potato; the rest of the chip is made from other ingredients. And therefore, since only the minority of the product is potato, the proper Beracha is "She’hakol," and not "Ha’adama." A separate question arises with regard to the barbeque flavored Pringles, which contain flour. Foods that contain flour could require the Beracha of "Mezonot," depending on the function the flour serves in the mixture. As the function of the flour in barbeque flavored Pringles is unclear, the Yalkut Yosef rules that one should eat this product only after reciting both "She’hakol" and "Mezonot" on other foods, in order to avoid this Halachic question.
Summary: According to Sephardic custom, the proper Beracha for mashed potatoes, potato pancakes, French fries and potato chips is "Ha’adama." Over Pringles potato chips, however, one recites "She’hakol." It is uncertain whether the barbeque flavored Pringles chips require "Mezonot" or "She’hakol," and therefore one should eat this product only after reciting both "She’hakol" and "Mezonot" on other foods.