Analytic / CONCEPT
Beta integral representation
Beta moments and integral formulas for the Kummer function.
Closed
DIRECT PREREQUISITES1
DIRECT CONSEQUENCES8
PROOF DEPTH1
DOCUMENT LINKS0
Real beta moments
RELATIONSHIP ATLAS
Every connection, in context.
Direct recorded relationships
Proof dependencyStructural affinityDocument link
Certified topology / UPSTREAM
Prerequisites
Certified topology / DOWNSTREAM
Consequences
- A modified Bessel ratio need not be log-concavetruth-dependency · Closed
- Coefficient convolution as a beta mixture meantruth-dependency · Closed
- Gamma ratios and differentiated seriestruth-dependency · Closed
- Gamma-normalized Kummer asymptoticstruth-dependency · Closed
- Kilbas–Saigo fractional kerneltruth-dependency · Closed
- Moment kerneltruth-dependency · Closed
- Pairing and the transformed Turaniantruth-dependency · Closed
- Sliding intervals and beta averagingtruth-dependency · Closed
RELATED KNOWLEDGE
Structural connections
- A modified Bessel ratio need not be log-concavestructural-affinity · Closed
- Beta integral endpoint asymptoticsstructural-affinity · Closed
- Coefficient convolution as a beta mixture meanstructural-affinity · Closed
- Gamma ratios and differentiated seriesstructural-affinity · Closed
- Gamma-normalized Kummer asymptoticsstructural-affinity · Closed
- Incomplete beta coefficientsstructural-affinity · Closed
- Increasing weightsstructural-affinity · Closed
- Kilbas–Saigo fractional kernelstructural-affinity · Closed
- Kummer reflectionstructural-affinity · Closed
- Logarithmic derivatives and finite parameter incrementsstructural-affinity · Closed
- Moment kernelstructural-affinity · Closed
- Normalized Bessel functionsstructural-affinity · Closed
- Pairing and the transformed Turanianstructural-affinity · Closed
- Positivity and comparisonstructural-affinity · Closed
- Sliding intervals and beta averagingstructural-affinity · Closed
- The entire Kummer seriesstructural-affinity · Closed
- The real Kilbas-Saigo functionstructural-affinity · Closed
- The upper parameter ratiostructural-affinity · Closed
Documents & exposition
None recorded in this release.
Other authored & advisory relationships
None recorded in this release.
LIBRARY / RELEASE VERSIONS
Content history
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