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A character first introduced in the late stages of Dragon Ball Z and given more agency in the non-canon Dragon Ball GT with quite a number of fans is Gohan's daughter, Pan, who is around twelve years old upon her introduction. She shares her mother Videl's headstrong personality, and sneaks onto a spaceship boarded by the (literally) rejuvenated Goku and teenage Trunks, embarking on a tough journey to collect the Black Star Dragon Balls that have been spread across the galaxy.
Alongside Goku and Trunks, Pan faces a host of tough situations and opponents; however, the young girl is not quite as strong as either of her companions and evidence of this is her lack of a Super Saiyan transformation despite her genetics granting her the propensity for such. In the last episode of Dragon Ball GT, an elderly Pan is shown cheering on her grandson, Goku Jr., at the 64th World Martial Arts Tournament – the Tenka'ichi Budōkai. Goku Jr., despite being a distant descendent of Goku, is capable of achieving the coveted transformation, but here's why Pan deserves it.
Potential
One thing that Pan's father became synonymous with is potential, with his incredible feats throughout his childhood, Gohan is the fighter who was the most likely to surpass Goku. While this never came to pass, his potential has been seemingly passed down to Pan, who in both her introductions in Dragon Ball Z and Dragon Ball Super, is capable of flight as a mere baby. While it is easy to credit her Saiyan constitution for her natural affinity for combat and fighting, Pan's human lineage is actually responsible for the vast majority of the aspects that make her such a high-potential prospect in the first place.
While Saiyans are naturally built to love fighting, Pan's human side is actually complementary to this as her mother, Videl, was once quite the fiery combatant and never shied away from a confrontation. Videl even took a heavy beating from a minion of Babidi's – an individual who was granted a supernatural ability boost from his affiliation with the Majin – and continued to put up a stand despite sustaining so much damage.
In fact, Videl had Spopovich on the ropes for the majority of their bout at the World Tournament, and probably would have killed him if he were a normal guy; however, the fight draws on for too long and an exhausted Videl is brutalized by Spopovich who toys with her until his colleague in evil, Yamu, tells him to stop messing around. Combining Gohan's immense potential and Saiyan blood with the fiery temperament of someone like Videl would create a Saiyan-human hybrid that is more human than Saiyan, but not necessarily at the cost of combat sense, unlike her father.
Pan's rambunctious personality puts her in a better position to harness her strength despite being only a quarter Saiyan, and as seen in the recent Dragon Ball Super: Super Hero film, Pan's potential is recognized by Gohan's teacher himself, Piccolo. Young Pan is capable of flight at a young age, which is something that even the full-blooded Goku had to learn how to do when he was younger, and as seen in final episodes of Dragon Ball Z and in the Dragon Ball Super: Super Hero film, her strength is far above that of a normal human even as a young child, and she is easily able to defeat grown men in seconds.
Ancestry Dot Z
One thing that was rather controversial, among various things in Dragon Ball GT, was the final episode which depicted the 64th World Martial Arts Tournament held in Age 889 – i.e. about 110 years after Pan's birth. An elderly Pan is in the audience, seated next to an individual clearly descended from Bulma, whose son, Vegeta Jr., is participating in the tournament. Vegeta Jr.'s opponent in the tournament is none other than Goku Jr., Pan's great-great-grandchild (or just grandchild depending on which dub you're asking). Goku Jr. and Vegeta Jr. are capable of transforming into Super Saiyans and do so during their bout; however, it's obvious that distant descendants of Pan would have their Saiyan blood further diluted with that of humans, and therefore have even less propensity towards Saiyan abilities and tendencies.
If one calculates their composition assuming that Goku Jr. is Pan's grandchild, then it would follow that he is only one-sixteenth Saiyan. Goku Jr.'s ability to transform into a Super Saiyan might imply the overt dominance of Saiyan genetics regardless of the ratio of Saiyan to human genetics. Mendelian genetics further complicate this story as dominance also denotes the existence of recessive genes and traits, meaning that it would fully be possible for certain Saiyan characteristics to select or skip certain members for reasons that aren't fully understood. However, Goku's ascension to Super Saiyan God required the power of five righteous Saiyans with Pan turning out to be the crucial final piece of the puzzle despite being unborn, which strengthens the "Saiyan dominance" idea of genetic inheritance in Dragon Ball and therefore, becomes a huge reason why Pan should be able to transform into a Super Saiyan. However, long before the arrival of Goku Jr., it was stated in the Daizenshū (official Dragon Ball guidebooks originally published in Japan) that no individual with less than a quarter of Saiyan blood would be able to assume the Super Saiyan transformation.
Saiyan Enough
Considering Pan's immense power for an infant/toddler, strong genes and her tenacious personality, not to mention the cheapening of the Super Saiyan transformation's base requirements through the easy achievement of the form by Goten, Trunks and the Universe 6 Saiyans, it would only make sense for a battle-ready combatant like herself to have the ability to transform. With Gohan's potential supposedly passed down to his daughter, having a Super Saiyan Pan may open up further possibilities regarding the character's significance to the story.
If it takes a good teacher less than a day to transform a Saiyan with no concept of the Super Saiyan transformation, then a combatant surrounded by some of the most powerful fighters in Universe 7; one who is the daughter of the first individual in the history of the Saiyans to ascend past a Super Saiyan should most definitely have the potential for the coveted transformation. If Goku Jr. could achieve the form despite his distant Saiyan heritage, then Pan should be well on her way. It might just need the right kind of motivation, but with her strong character, decent base power and Piccolo training her, it's clear the young Saiyan will be a brilliant fighter worthy of becoming a Super Saiyan soon enough.