Modular Discriminant Delta Calculator
FiniteqΠn≤N(1−q^n)^24 standard modular discriminantΔ, realqbranch, no full infinite product error certificate, underflow rejected. Explicit bounded resource/branch and actual observations or independently verified parameters; no unproved infinite assertion certified.
Description
The modular discriminant has a q-product whose finite truncation omits later factors.
The modular discriminant has a q-product whose finite truncation omits later factors.1
This tool evaluates that truncated product on a real positive q branch without certifying the infinite value.
When to use Modular Discriminant Delta Calculator
This tool evaluates that truncated product on a real positive q branch without certifying the infinite value.
How to use Modular Discriminant Delta Calculator and how it works
- Prepare real q, product cutoff, using the input definitions and matching units below.
- Enter the required fields and run Modular Discriminant Delta Calculator.
- Read result.truncatedDelta using the units, signs and ordering explained below.
- Correct any rejected inputs and rerun; interpret the result within the stated model and its assumptions.
| Input field | Meaning | Value type | Requirement |
|---|---|---|---|
| actualRealQ | Real product variable q, strictly between zero and one. | number | Required; strictly positive; finite; other constraints below |
| actualProductCutoff | Actual Product Cutoff. Use the units and matching context stated in the calculation below. | number | Required; integer 1–10000; finite; other constraints below |
Require real q strictly between 0 and 1 and product cutoff integer 1–10000. Calculate log(q)+24*sum(log1p(-q^n)) through cutoff and exponentiate. Return the truncated real Delta product. Underflow to zero and nonfinite results are rejected by expFinite; no infinite-tail or interval-rounding certificate is returned.
truncatedDelta=q*product((1-q^n)^24,n=1..N) Apply the input ordering, units and branch conditions stated above.
| Output field | Meaning | Value type |
|---|---|---|
| result | Object containing the calculated or selected fields below. | object |
| result.truncatedDelta | Finite modular Delta product under the stated branch and truncation; no additional numerical certificate. | number |
{
"input": {
"actualRealQ": 0.01,
"actualProductCutoff": 1
},
"output": {
"result": {
"truncatedDelta": 0.00785678140807219
}
}
}Limitations and assumptions
The calculation uses the supplied observations and model inputs. It does not collect measurements, select a reference population or coefficient, or establish that the model applies to the actual case. The stated branch conditions and output units remain part of the result.
All fields require explicit values. Unexpected fields, wrong types, nonfinite numbers and sparse arrays are rejected. Alignment, bounds and supported-token rules are explained above; extremely large inputs or nonfinite results can also fail. Input errors differ from successful false comparisons, unavailable-domain flags and empty match lists.
Alternative or Complementary methods
Use Rogers-Ramanujan Continued Fraction Approximation for a complementary operation: The Rogers-Ramanujan continued fraction has an infinite nested structure and a specified leading q factor.
Use Mock Theta Function Approximation for a complementary operation: Ramanujan's third-order mock theta f is one named function within a broader family.
References
-
Modular Discriminant Delta Calculator — tool.io
Similar or alternative tools
- Rogers-Ramanujan Continued Fraction Approximation
The Rogers-Ramanujan continued fraction has an infinite nested structure and a specified leading q factor.
- Mock Theta Function Approximation
Ramanujan's third-order mock theta f is one named function within a broader family.