Equation 3 · Function Calling, MCP, and the Other Ways to Give a Model Tools
What does this equation mean?
Read the formula alongside the article passage below. Each part has a deeper page with its role in the equation, the supporting passage and nearby citations.
This equation gives an approximation: it relates the quantities while allowing an approximation. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.
Read it piece by piece
Symbol I_bespoke
espoke is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
Symbol N
N is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
subscript
The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.
How to interpret it
Its accuracy depends on the assumptions and range of use described in the article.
What the article says around this equation
That combinatorial framing is worth making explicit, as a stylized model rather than a measured cost curve. Call the number of distinct model-facing client applications M and the number of distinct external tools or data sources N . Absent any shared protocol, a connector is needed for each pairing that is actually wanted, so the number of bespoke integrations that must be built and separately kept current scales as . A protocol that both sides target once, instead, lets each side write a single adapter to the shared standard, so the count becomes
Sources cited in the article section
- [5] Introducing the Model Context Protocol ↗
- [6] Specification ↗
- [7] Server Features: Tools ↗
- [8] Authorization ↗
- [4] Tool use with Claude ↗
These citations give research context. Read each source to check which claims it supports.
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