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

= 1 ʋ [ − (0) ʋ + { ( )}] A New Integral Transform Called “Saxena & Gupta Transform” and Relation between New Transform and other Integral Transforms { ′ ( )} = (ʋ) ʋ − (0) ʋ 2 … (2.9) Second derivative { ′′ ( )} = 1 ʋ { ′ ( )} − ′(0) ʋ 2 = 1 ʋ [ (ʋ) ʋ − (0) ʋ 2 ] − ′(0) ʋ 2 { ′′ ( )} = (ʋ) ʋ 2 − (0) ʋ 3 − ′ (0) ʋ 2 … (2.10) Nth derivative { ( )} = (ʋ) ʋ − (0) ʋ +1 − ′(0) ʋ − ′′(0) ʋ −1 { ( )} = (ʋ) ʋ − ∑ (0) ʋ +1− −1 =0 … (2.11) Theorem 2: If the following [ ( )] is well defined then [∫ ( ) 0 ] = ʋ 2 { } Proof: Suppose that g(t-τ)=1 then [∫ ( ) 0 ] = [∫ ( − ) ( ) 0 ] = [ ∗ ] = ʋ 2 [ ] [ ] The New transform of Integral © 2023 Global Journals 1 Year 2023 14 Global Journal of Science Frontier Research Volume XXIII Issue ersion I V ( F ) N otes IV v)