Problem No 19 on Beta Function - Beta and Gamma Function - Engineering Mathematics - 2

TL;DR

The video demonstrates how to prove the property of the gamma function using mathematical properties and formulas.

Transcript

hey friends so here we will prove the property of gamma function and for that i have a question for you that is gamma 3 by 2 minus x into gamma 3 by 2 plus x is equal to 1 by 4 minus x square whole into pi 6 pi x now the question is how to prove this so if you see the left hand side we have two gamma functions and for the gamma functions we have n ... Read More

Key Insights

• 👻 The property of the gamma function allows for simplification of equations involving gamma functions.
• 😀 The value of p in the gamma function can be chosen strategically to match the required values for simplification.
• 🤨 The value of pi plays a significant role in the simplification process.
• ❓ The cosine function is used to further simplify the equation and obtain the final result.
• 🎮 The video demonstrates the importance of mathematical properties in solving complex equations.
• 😒 The use of gamma function and its properties is essential in engineering mathematics.
• 🎮 The video suggests visiting a website (ek.com) for more comprehensive learning on the concepts of beta and gamma functions.

Questions & Answers

Q: How does the property of the gamma function help simplify the equation?

The property of the gamma function allows us to substitute the value of n in the function and simplify it further using mathematical operations.

Q: Why is the value of p chosen as 1/2 + x in the equation?

The value of p is chosen as 1/2 + x to match the values required by the property of gamma function, which is used to further simplify the equation.

Q: How is the value of pi introduced in the equation?

The value of pi is introduced in the equation through the property of gamma function, which involves the ratio of gamma functions and the sine of pi.

Q: What is the significance of simplifying the equation using the cosine function?

Simplifying the equation using the cosine function allows for further simplification of the expression and obtaining the final result in terms of the product of pi and the sign function.

Summary & Key Takeaways

• The video introduces a question regarding the gamma function and its property.

• The left-hand side of the equation is simplified using the property of the gamma function.

• The right-hand side of the equation is evaluated using the values of gamma and sine functions.