The link you sent me did not disprove my theory

Yes it did.

and please don't reference wikipedia. I know you can do much better.

Wikipedia is an excellent resource to reference for trivial facts. Follow the links from the wikipedia page and look at the actual sources if you really want to pretend you are too cool for wikipedia itself. (That is, the wikipedia snub is an intellectual one-upmanship move that is miscalibrated with respect to this particular social environment.)

The problem is that nobody really knows exactly what rays humans need to make vitamin D.

I don't believe you.

Also, can you find a single large-scale (I would say 1000+, but that's a relatively low number. A real large scale study is more like 10,000+...) study that shows lamps produce significant amounts of V.D.?

If you are going to specify a single number to represent standard of evidence for a study you ought to specify a the statistical significance required (for a given effect size). (An alternative like likelihood ratio would also work.)

Of course even then you cannot by force of will negate the fact that smaller, less conclusive studies still provide evidence. Weaker evidence but still evidence. Even a well designed study of a single individual is informative.

The link you sent me did not disprove my theory

See this part, emphasis mine.

Vitamin D3 is made in the skin when 7-dehydrocholesterol reacts with ultraviolet light (UVB) at wavelengths between 270 and 300 nm, with peak synthesis occurring between 295 and 297 nm. These wavelengths are present in sunlight when the UV index is greater than three, as well as in the light emitted by the UV lamps in tanning beds (which produce ultraviolet primarily in the UVA spectrum, but typically produce 4% to 10% of the total UV emissions as UVB).

UV lamps in tanning beds produce UV light of the right frequency to stimulate vitamin D production. They have to, in order to do what they do.

and please don't reference wikipedia. I know you can do much better.

A trivial Googling shows several sources claiming that tanning beds and lamps generate UVB.

The problem is that nobody really knows exactly what rays humans need to make vitamin D.

UVB light. See above.

Also, can you find a single large-scale (I would say 1000+, but that's a relatively low number. A real large scale study is more like 10,000+...) study that shows lamps produce significant amounts of V.D.?

Reasonably large studies have been done on treating rickets, a vitamin D deficiency, with ultraviolet lamps. Unsurprisingly, it works.

Now then, what evidence do you have that 1) we don't know what wavelengths of light stimulate vitamin D production; 2) we can't build lamps that produce those wavelengths; and 3) that the lamps we have do more harm than good.

Consider 3) in the light of the vast advances in curing rickets since the 19th century.

My relative works in a large hospital and has given many (cancer) patients vitamin D pills

Have you moved from rejecting mere wikipedia references and demanding studies with 10k+ to appealing to the speculation of your relative?