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In this paper we consider spaces of GL(4, R)-Whittaker functions, which are special functions that arise in the study of GL(4, R) automorphic forms. Our main result is to determine explicitly the series expansion for a GL(4, R)-Whittaker function that is "fundamental," in that it may be used to generate a basis for the space of all GL(4, K)-Whittaker functions of fixed eigenvalues. The series that we find in the case of GL(4, R) is particularly interesting in that its coefficients are notdoi:10.1126/science.96.2496.399-b pmid:17735635 fatcat:3owfqvqjfzbn7insbkp2jo7crq