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Berndt, Bruce C. Yi, Jinhee 2015-09-28T15:19:30Z 2015-09-28T15:19:30Z 10000-01-01 2001 2001 We introduce also two parametrizations hk,n and h'k,n of the theta-function 4q . For q=e2piz , Im z > 0, define 4q : =fq,q=n =-infinityinfinityqn2 =:q30,2z , where q3 is classical theta function. For any positive real numbers n and k, define hk,n=4e-p n/k k1/44e-p nk=q 30,-n/k k1/4q30, -nk and h'k,n=4 -e-2pn/k k1/44-e-2p nk =q30,1+2-n/ kk1/4q 30,1+2-nk . We show how they are connected with rk,n, r'k,n and Ramanujan-Weber class invariants and give some new theta-function identities. In addition, we establish some formulas for hk,n and h'k,n by using those theta-function identities and find some values of hk,n and h'k,n . Finally, we offer explicit formulas for 4-e-np and 4e-np for any positive real numbers n. We give some examples. Made available in DSpace on 2015-09-28T15:19:30Z (GMT). No. of bitstreams: 2 license.txt: 4848 bytes, checksum: 96035ab3f5e1c23cc7138a224ce498bd (MD5) 3017261.pdf: 4334866 bytes, checksum: 3563146fd088258751ea49489bb21e14 (MD5) Previous issue date: 2001 Embargo set by: Seth Robbins for item 88061 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs U of I Only 157 p. Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2001. http://hdl.handle.net/2142/86780 (MiAaPQ)AAI3017261 eng Mathematics The Construction and Applications of Modular Equations text Mathematics Mathematics University of Illinois at Urbana-Champaign Dissertation Ph.D.