Kashmiri veterinarian finds solution to mathematical problem

Srinagar, Dec 4 (UNI) A Kashmiri veterinarian has succeeded in finding a solution to a long-standing mathematical problem and come up with a new theorem.

Dr Shabir Ahmad Mir, a Professor and Head, Division of Veterinary Pharmacology and Toxicology, Faculty of Veterinary Sciences, Sher-i-Kashmir University of Agricultural Sciences and Technology (SKUAST), has devised ''Mir's Trinomial Expansion Theorem'' that precisely determines an rth term and other functions related to the trinomial expansion.

The theorem introduces Exponent Array Model (EAM) with set of equations that permit hierarchial arrangement of expanded terms for precise location on an rth term.

The work has been published in the September 2006 issue (Volume LXIV, Number 1-2) of the journal of Mathematika Sciences Society of India titled Pure And Applied Mathematika Sciences.

In the paper, Mir explains that Binomial Expansion Theorem is well known and finds place in nearly all mathematical textbooks.

The theorem is employed to expand any binomial function of order n i.e. (+ a + b)*n, and to precisely determine rth term with its coefficients, he adds.

However, Mir says such a technique did not exist for expansion of a trinomial function of order n i.e. (+ a + b + c)An, nor there has been any technique to determine precisely rth term.

At present, the practice is to use Binomial theorem to expand any trinomial function by reducing the trinomial to a binomial form, the paper says.

However, the procedure to do so is very cumbersome, indirect and puts expanded secondary terms in a haphazard order thereby jeopardising precise location of an rth term for the trinomial function, says Mir.

Thus, a need to develop an effective and direct technique for expansion of a trinomial function was mooted, the paper adds.

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