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I have problem of alignment in the following, please check and suggest solution:

            e^{at}, & 0\leq t<\infty,\\
            e^{bt}, & -\infty<t<0.                              
    for m=1, 2, 3, \ldots, n=1, 2, 3, \ldots, k'=0, 1, 2, \ldots.

In output equations doesn't appear in the same line as of item number, appears at center of second line. I want it to appear in the same line with left alignment and corresponding equation numbers to right of page.

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Welcome to TeX.sx! In its current form, your 'question' doesn't actually ask a question. Please update it with something specific. It would also be best to make your code into a complete minimal working example (MWE) – cmhughes Feb 7 '13 at 18:12
Does this answer help? – Ian Thompson Feb 7 '13 at 21:21
@ cmhughes I have made some changes to question, hope it will be clear now. – Madhu Feb 7 '13 at 21:43
@ Ian, I checked it. sorry, it is not solving my problem. – Madhu Feb 7 '13 at 21:46
Another suggestion: Displaying an equation in a list. – Hendrik Vogt Feb 7 '13 at 22:00

You could use the flalign environment from the amsmath package with the numbers in the first column.

\newcommand\leftno{\addtocounter{thing}{1} \arabic{thing}.\quad }
\leftno &   \kappa_{a,b}(t)=
   e^{at}, & 0\leq t<\infty,\\
   e^{bt}, & -\infty<t<0.                              
    \label{eq:kappa-ab-t} & \\
\leftno & \beta(x)=\frac{x^m}{\mu_n^{2k'-1}}
        \label{eq:beta-x} & \\
\setcounter{thing}{27} %Test alignment of two digit numbers
\leftno & \beta(x)=\frac{x^m}{\mu_n^{2k'-1}} & 
    for m=1, 2, 3, \ldots, n=1, 2, 3, \ldots, k'=0, 1, 2, \ldots.

Numbering on both the left- and right-hand sides looks rather strange, though.

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@ Ian, Thanks. This has solved my problem. Its listing of some functions under a chapter which will be referred further in other chapters, so may feel at first strange. – Madhu Feb 7 '13 at 23:20

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