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Rabbi Tzvi Hirsch ben Yaakov Ashkenazi (1656, Moravia May 2, 1718, Lviv 'צבי הירש בן יעקב אשכנזי', known as the Chacham Tzvi (after responsa by the same title), for some time rabbi of Amsterdam, was a resolute opponent of the followers of the false messiah, Sabbatai Zevi.
He was an iconoclast and had a chequered career, owing to his independence of character. He visited many lands, including England, where he wielded much influence. His responsa are held in high esteem. He was the grandson of Elijah Ba'al Shem of Chelm. cont. Wikipedia
The Baal Shem Tov is claimed to have said about the family: that there are three famous families of Israel that are pure, generation after generation: Horowitz, Margoliot and Shapiro ." and Rappaport, who are Kohanim.
Rabbi Tzvi Hersh Ashkenzy, 1660-1718, known as the “Chacham Tzvi”, was the son of Rabbi Yaakov Ashkenazy, a son of Rabbi Benyamin Zev Zak of Vilna.
Yaakov Ashkenazy was married to Nechamah, the daughter of Rabbi Efraim Hakohen of Vilna, the author of “Shaarei Efraim”.
Several books claim that the wife of Benyamin Zak was a daughter of Rabbi Yaakov of Lublin, the father of Rabbi Avraham Yehoshua Heshel, known as “Reb Heshel of Krakow”.
If this was so, then the Chacham Tzvi would be descended from Rashi and thence from King David through Yaakov of Lublin’s relationships with various families of Rashi Descent.
Rabbi Shlomo Englard (Bnei Brak, Israel), an authority on Rabbinic genealogy, specialising in identifying errors in printed genealogies, disputes the claim that the Chacham Tzvi’s paternal grandfather was a daughter of Yaakov of Lublin. Englard presents convincing and decisive arguments to support his claim.
Another claim which might have provided the Chacham Tzvi with Davidic descent is that his maternal grandfather, Efraim Hakohen was descended from Efraim Fishel a son-in-law of Rabbi Shlomo Luria the “Maharshal” who was descended from Rashi. Englard denies this relationship.
The wife of the Chacham Tzvi, Sarah, was a daughter of Rabbi Meshullum Zalmen Mirels Neumark. An erroneous claim by several genealogists was that a female ancestor of Meshullum Zalmen’s was a daughter of Rabbi Efraim Zalmen Schorr, whose wife was a Katzenellenbogen and thereby of Rashi and Davidic descent. Englard brings evidence to disprove this claim.
One source, “Elef Margaliot” by Rabbi Meir Wunder includes a genealogical table of the Mirels-Neumark-Teomim-Frankel family indicating descent from Rashi. However no evidence of this claim is presented.
Englard published his arguments in “Tzfunot” #13 and in a collection of his articles published by Tzfunot Yuchsin Institute, Summer 2004.
I have checked Englards sources and researched over twenty books which include details of the personalities referred to above. My conclusions agree with Englard and I can see no way by which the Chacham Tzvi or his wife were descendants of Rashi and King David. Furthuremore I have seen no such claim by his descendants in the books which they wrote, for example the Chacham Tzvi’s son Rabbi Yaakov Emden (the “Yavetz”).
Of course, it is highly likely that all Ashkenazy Jews are descended from Rashi, as well as all Jews living in Germany and France at Rashi’s time. This is based on mathematical calculations of probability.
The descendants of the Chacham Tzvi might be consoled by what the Baal Shem Tov is claimed to have said about the family: that they are one of the three families who are “clean” generation after generation. (“Binyan Ariel” P. Mayers, Haag, Holland, published in Jerusalem in 2005).
Chaim Freedman's Geneaology Blog, Petah Tikvah, Israel