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March 1, 2026Arizona Birds0 citations

Pascal-like matrix with double factorial binomial coefficients

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GKGonca Kızılaslan

Key Points

  • The research aims to explore a new variation of a Pascal-like matrix using double factorial binomial coefficients and its properties.
  • Defined a new Pascal-like matrix with double factorial binomial coefficients.
  • Calculated the inverse of the proposed matrix.
  • Derived explicit representations for the matrix's powers under various exponent types (integer, rational, irrational).
  • Generalized the matrix and established new identities.
  • Demonstrated key properties of the new matrix variant.
  • Successfully calculated the inverse of the matrix.
  • Obtained explicit forms for powers of the matrix for different types of exponents.
  • Presented several new mathematical identities related to the generalized matrix.

Abstract

We introduce a variation of a Pascal-like matrix which includes double factorial binomial coefficients and show that it satisfies several properties. We find the inverse of the defined matrix and derive explicit representations of the powers of it for the integer, rational and irrational exponents. Finally, we give a generalization of this matrix and obtain some identities.

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Cite This Study

Gonca Kızılaslan (2023) studied this question.

synapsesocial.com/papers/69a3d856ec16d51705d2f1a9https://doi.org/10.1007/s13226-023-00496
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