Kilbas–Saigo fractional kernel

Abstract

Fractional Gamma-ratio kernel certificate.

Theorem 1.1 (Zero increment).

Lean statement: D5/S3/Analytic/KilbasSaigo/Certificate.certificate

Proof. Machine-checked in Lean as D5/S3/Analytic/KilbasSaigo/Certificate.certificate (✓ std3). ∎

Source. Repository-derived.

Commentary.

The fractional kernel is defined from the affine Gamma-ratio parameters. When the increment exponent is zero, the integrand vanishes and the two Gamma-ratio terms coincide.

References

• Truth anchor: D5/S3/Analytic/KilbasSaigo/Certificate.certificate
• Dependency: D5/S3/Analytic/KilbasSaigo/Defs
• Dependency: D5/S3/Analytic/KummerRatio/BetaIntegral