What's New
About the Project
NIST
12 Parabolic Cylinder FunctionsProperties

§12.8 Recurrence Relations and Derivatives

Contents

§12.8(i) Recurrence Relations

12.8.1 zU(a,z)-U(a-1,z)+(a+12)U(a+1,z) =0,
12.8.2 U(a,z)+12zU(a,z)+(a+12)U(a+1,z) =0,
12.8.3 U(a,z)-12zU(a,z)+U(a-1,z) =0,
12.8.4 2U(a,z)+U(a-1,z)+(a+12)U(a+1,z) =0.

(12.8.1)–(12.8.4) are also satisfied by U¯(a,z).

12.8.5 zV(a,z)-V(a+1,z)+(a-12)V(a-1,z) =0,
12.8.6 V(a,z)-12zV(a,z)-(a-12)V(a-1,z) =0,
12.8.7 V(a,z)+12zV(a,z)-V(a+1,z) =0,
12.8.8 2V(a,z)-V(a+1,z)-(a-12)V(a-1,z) =0.

§12.8(ii) Derivatives