Global Journal of Science Frontier Research, F: Mathematics and Decision Science, Volume 23 Issue 4

= ʋ 2 [ ] Let the function ̅( ʋ )=̅ {F} is the transform of the function ( ) , then ( ) is called the inverse transform ̅( ʋ ) and we will write it as A New Integral Transform Called “Saxena & Gupta Transform” and Relation between New Transform and other Integral Transforms ( ) = −1 {̅ (ʋ)} The inverse transform has the linear combination property 1. when ( ) = 1 then 1 ʋ ∫ − (ʋ ) = 1 ∞ 0 ∫ −∞ 0 . 1 = 1/ʋ[− − ] 0 ∞ = 1 / ʋ 2. when ( ) = then 1 ʋ ∫ − (ʋ ) = 1 ʋ ∞ 0 ∫ − ∞ 0 . ʋ = = 1/ʋ[(− − 1) − ] 0 ∞ = 1 ʋ 3. when ( ) = 2 then 1 ʋ ∫ − (ʋ ) = 1 ʋ ∞ 0 ∫ − ∞ 0 . ʋ 2 2 = 1 ʋ [(− 2 − 2 − 2) − ] 0 ∞ = 2 ʋ 4. when ( ) = then 1 ʋ ∫ − ( ) = 1 ʋ ∞ 0 ∫ −∞ 0 . ʋ = −1 Г(n+1) 5. when ( ) = then 1 ʋ ∫ − (ʋ ) = 1 ʋ ∞ 0 ∫ − ∞ 0 . ʋ The inverse of New transform Definition: Note: Solution of some elementary function N otes 1 Year 2023 15 Frontier Research Volume XXIII Issue ersion I V ( F ) Science © 2023 Global Journals Global Journal of IV vi) vii)