Srivastava, G. S.; Kasana, H. S. A note on entire functions of irregular (p,q)-growth. (English) Zbl 0588.30031 Jñānabha 15, 55-63 (1985). For a given entire function f the lower (p,q)-order is defined as \[ \lambda =\lambda (p,q)=\lim \inf_{r\to \infty}\log^{(p)}M(r,f)/\log^{(q)}r, \] where \(M(r,f)=\max_{| z| =r}| f(z)|\) and \(\log^{(q)}r\) denotes the qth iterate of log r. If f has lower (p,q)-order \(\lambda\) (where \(\lambda >0\) if \(p>q\) and \(\lambda >1\) if \(p=q)\), a lower (p,q)-proximate order \(\lambda\) (r) is defined if \[ (i)\quad \lim_{r\to \infty}\lambda (r)=\lambda,\quad (ii)\quad \lim_{r\to \infty}\lambda (r)(\log^{(q)}r)(\log^{(q- 1)}r)...(\log r)r=0, \] and \[ (iii)\quad \lim \inf_{r\to \infty}(\log^{(p-1)}M(r,f))/(\log^{(q-1)}r)^{\lambda (r)}=t_{\lambda} \] where \(0<t_{\lambda}<\infty\). Then \(t_{\lambda}\) is defined as the generalized \(\lambda\) (p,q)-type of f with respect to \(\lambda\) (r). A necessary and sufficient condition for f to be of given generalized \(\lambda\) (p,q)-type is found in terms of the Taylor coefficients of f under certain restrictions. Reviewer: C.N.Linden MSC: 30D20 Entire functions of one complex variable (general theory) 30D15 Special classes of entire functions of one complex variable and growth estimates Keywords:(p,q)-order; lower (p,q)-order; (p,q)-proximate order; \(\lambda \) (p,q)- type; Taylor coefficients PDFBibTeX XMLCite \textit{G. S. Srivastava} and \textit{H. S. Kasana}, Jñānābha 15, 55--63 (1985; Zbl 0588.30031)