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We give a new proof for a product formula of Jacobi which turns out to be equivalent to a $q$-trigonometric product which was stated without proof by Gosper. We apply… Click to show full abstract
We give a new proof for a product formula of Jacobi which turns out to be equivalent to a $q$-trigonometric product which was stated without proof by Gosper. We apply this formula to derive a $q$-analogue for the Gauss multiplication formula for the gamma function. Furthermore, we give explicit formulas for short products of $q$-gamma functions.
Keywords:
jacobi;
product jacobi;
product;
applications gamma;
theta product;
jacobi applications
Journal Title: Journal of Mathematical Analysis and Applications
Year Published: 2019
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Journal Title: Journal of Mathematical Analysis and Applications
Year Published: 2019
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!