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The Author of Ratna Mañjuṣā and the Binomial Expansion
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It has also been observed that different rules for the formation of the binomial coefficients, arranged in their proper sequence i.e., the (so called) Pascal's triangle, have been given by various authorities on metrical sciences (and mathematicians),
The Suct Prast ära.
The Ratna Mañjūṣā contains two rules for the formation of the binomial coefficients. The first rule gives a process for the formation of the sequence given earlier by Acarya Jayadeva, a Jain authority on metrical sciences and others and is known as the sūcī prast ära in metric.
Alternative Rule.
The Ratna Mañjūṣā contains an alternative rule for the formation of the sequence of binomial coefficients. The rule may be translated as given below.
"Cells are formed in rows such that their number (in the first row) is one more than the number of letters in the metre. These (i.e., the numbers of cells in respective rows) are in an arithmetic series and also less by one (in successive, lower (rows).
Sum of numbers in two consecutive lower cells is written in the upper cell.
This is the process for the formation of the khanda-meru for a metre as brought to light by Punnagacandra.8
The following figure (for n=4) illustrates the rule.
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Rm., viii, 16.
Rm., viii, 11 (p. 39). The text is, सैका मेकगणोज्ज्वलामभिमतच्छन्दोक्ष रागारिकाम्
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एकां श्रेणिमुपक्षिपन्नधस्तोऽप्येकैक हीनाश्च ताः
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