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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 저널정보
- 장전수학회 Advanced Studies in Contemporary Mathematics Advanced Studies in Contemporary Mathematics Vol.26 No.2
- 발행연도
- 2016.1
- 수록면
- 305 - 320 (16page)
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초록· 키워드
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We continue our investigations of the Γq-function and its relative, the Ψq function. A formula for the quotient of singular values of Γq functions is found by a procedure with limits of the fourth theta function. The extreme values of Γq functions are tabulated, and a theorem for the inverse of Γq is stated. Referring to Artin, it is shown that both Ψq and ｜ Γq｜ are strictly increasing. The second part of the paper is devoted to a q-analogue of the tenth chapter in Ramanujan's second notebook. Some of these formulas have multiple q-analogues; the proofs work swiftly with differentiation or logarithmic differentiation, and the right hand sides contain generalized Γq or Ψq functions. Sometimes q-analogues in terms of the rst theta function turn up; these also have multiple forms.
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