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Bernoulli polynomials

Relationships observed in Wikidata. Connections do not establish verification or source support.

Release: sha256:f33228901a35b0683356002a46df9ceb11f399d05f17abb5c7c78256cbf38ba7

Provider: Wikidata · graph projection only.

OBSERVED · GRAPH-PROJECTION · NOT ADMITTED · NOT VERIFIED · NOT SUPPORT

Edge identity is the provider property id (for example P31). It is not a Counterpedia predicate.

Development requests are not available on this deployment. The observed entity and its graph links remain readable.

Relationships of Bernoulli polynomials

Show relationship types (drawing only; the text lists are unaffected)
instance of (Observed provider relationships)named after (Observed provider relationships)Relationship label not yet available (Observed provider relationships)instance of (Observed provider relationships)Commons category (Observed provider relationships)Relationship label not yet available (Observed provider relationships)notable work (Observed provider relationships)Bernoulli polynomials — Wikidata entity (Q2346201)BernoullipolynomialsWIKIDATA ENTITYpolynomial sequence — Wikidata entity (Q1052437)polynomialsequenceWIKIDATA ENTITYJacob Bernoulli — Wikidata entity (Q122392)Jacob BernoulliWIKIDATA ENTITYB_m(x)= \sum_{n=0}^m \frac{1}{n+1} \sum_{k=0}^n (-1)^k {n \choose k} (x+k)^m — Literal value (wikidata:literal:2:B_m(x)= \sum_{n=0}^m \frac{1}{n+1} \sum_{k=0}^n (-1)^k {n \choose k} (x+k)^m)B_m(x)=\sum_{n=0}^m…LITERAL VALUEmathematical concept — Wikidata entity (Q24034552)mathematicalconceptWIKIDATA ENTITYBernoulli polynomials — Literal value (wikidata:literal:4:Bernoulli polynomials)BernoullipolynomialsLITERAL VALUEWikiProject Mathematics — Wikidata entity (Q8487137)WikiProjectMathematicsWIKIDATA ENTITY

Legend

  • Governed record relationships (solid)
  • Countergraph traversal (dashed)
  • Countergraph evidence (dotted)
  • Observed provider relationships (dash-dot)
  • Structurally derived (sparse dots)

Node shape identifies node kind only. Size, color, and position carry no meaning beyond hop distance from the root.

A line means a supported artifact carried an explicit structured relation. It does not mean the relation is true, admitted, verified, or authoritative.

Graph as text

Nodes (7)

  • Bernoulli polynomials — Wikidata entity
    Technical details
    node_id
    wikidata:entity:Q2346201
    stable_ref
    Q2346201
    node_kind
    wikidata_entity
    plane
    provider_observed
    qid
    Q2346201
    provider
    wikidata
    entity_href
    /entries/wikidata/Q2346201
  • polynomial sequence — Wikidata entity
    Technical details
    node_id
    wikidata:entity:Q1052437
    stable_ref
    Q1052437
    node_kind
    wikidata_entity
    plane
    provider_observed
    qid
    Q1052437
    provider
    wikidata
    entity_href
    /entries/wikidata/Q1052437
  • Jacob Bernoulli — Wikidata entity
    Technical details
    node_id
    wikidata:entity:Q122392
    stable_ref
    Q122392
    node_kind
    wikidata_entity
    plane
    provider_observed
    qid
    Q122392
    provider
    wikidata
    entity_href
    /entries/wikidata/Q122392
  • B_m(x)= \sum_{n=0}^m \frac{1}{n+1} \sum_{k=0}^n (-1)^k {n \choose k} (x+k)^m — Literal value
    Technical details
    node_id
    wikidata:literal:2:B_m(x)= \sum_{n=0}^m \frac{1}{n+1} \sum_{k=0}^n (-1)^k {n \choose k} (x+k)^m
    stable_ref
    wikidata:literal:2:B_m(x)= \sum_{n=0}^m \frac{1}{n+1} \sum_{k=0}^n (-1)^k {n \choose k} (x+k)^m
    node_kind
    wikidata_literal
    plane
    provider_observed
  • mathematical concept — Wikidata entity
    Technical details
    node_id
    wikidata:entity:Q24034552
    stable_ref
    Q24034552
    node_kind
    wikidata_entity
    plane
    provider_observed
    qid
    Q24034552
    provider
    wikidata
    entity_href
    /entries/wikidata/Q24034552
  • Bernoulli polynomials — Literal value
    Technical details
    node_id
    wikidata:literal:4:Bernoulli polynomials
    stable_ref
    wikidata:literal:4:Bernoulli polynomials
    node_kind
    wikidata_literal
    plane
    provider_observed
  • WikiProject Mathematics — Wikidata entity
    Technical details
    node_id
    wikidata:entity:Q8487137
    stable_ref
    Q8487137
    node_kind
    wikidata_entity
    plane
    provider_observed
    qid
    Q8487137
    provider
    wikidata
    entity_href
    /entries/wikidata/Q8487137

Edges (7)

  • Bernoulli polynomials — instance of → polynomial sequence — Observed provider relationships
    Technical details
    machine_predicate
    P31
    predicate_ref
    wikidata:property:P31
    provider
    wikidata
    provider_direction
    outgoing
    plane
    provider_observed
    edge_id
    wikidata:relation:0:P31
    release_ref
    sha256:f33228901a35b0683356002a46df9ceb11f399d05f17abb5c7c78256cbf38ba7
  • Bernoulli polynomials — named after → Jacob Bernoulli — Observed provider relationships
    Technical details
    machine_predicate
    P138
    predicate_ref
    wikidata:property:P138
    provider
    wikidata
    provider_direction
    outgoing
    plane
    provider_observed
    edge_id
    wikidata:relation:1:P138
    release_ref
    sha256:f33228901a35b0683356002a46df9ceb11f399d05f17abb5c7c78256cbf38ba7
  • Bernoulli polynomials — Relationship label not yet available → B_m(x)= \sum_{n=0}^m \frac{1}{n+1} \sum_{k=0}^n (-1)^k {n \choose k} (x+k)^m — Observed provider relationships
    Technical details
    machine_predicate
    P2534
    predicate_ref
    wikidata:property:P2534
    provider
    wikidata
    provider_direction
    outgoing
    plane
    provider_observed
    edge_id
    wikidata:relation:2:P2534
    release_ref
    sha256:f33228901a35b0683356002a46df9ceb11f399d05f17abb5c7c78256cbf38ba7
  • Bernoulli polynomials — instance of → mathematical concept — Observed provider relationships
    Technical details
    machine_predicate
    P31
    predicate_ref
    wikidata:property:P31
    provider
    wikidata
    provider_direction
    outgoing
    plane
    provider_observed
    edge_id
    wikidata:relation:3:P31
    release_ref
    sha256:f33228901a35b0683356002a46df9ceb11f399d05f17abb5c7c78256cbf38ba7
  • Bernoulli polynomials — Commons category → Bernoulli polynomials — Observed provider relationships
    Technical details
    machine_predicate
    P373
    predicate_ref
    wikidata:property:P373
    provider
    wikidata
    provider_direction
    outgoing
    plane
    provider_observed
    edge_id
    wikidata:relation:4:P373
    release_ref
    sha256:f33228901a35b0683356002a46df9ceb11f399d05f17abb5c7c78256cbf38ba7
  • Bernoulli polynomials — Relationship label not yet available → WikiProject Mathematics — Observed provider relationships
    Technical details
    machine_predicate
    P6104
    predicate_ref
    wikidata:property:P6104
    provider
    wikidata
    provider_direction
    outgoing
    plane
    provider_observed
    edge_id
    wikidata:relation:5:P6104
    release_ref
    sha256:f33228901a35b0683356002a46df9ceb11f399d05f17abb5c7c78256cbf38ba7
  • Jacob Bernoulli — notable work → Bernoulli polynomials — Observed provider relationships
    Technical details
    machine_predicate
    P800
    predicate_ref
    wikidata:property:P800
    provider
    wikidata
    provider_direction
    incoming
    plane
    provider_observed
    edge_id
    wikidata:relation:6:P800
    release_ref
    sha256:f33228901a35b0683356002a46df9ceb11f399d05f17abb5c7c78256cbf38ba7

Reader shortcuts (not graph edges) (0)

    Unresolved references (0)

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