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Gamma Function Calculator — result sheet
Evaluate the Gamma function Γ(x) and its natural logarithm for a positive real input.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: Γ(x)=∫₀∞ t^(x−1)e^(−t)dt for x>0; for positive integers, Γ(n)=(n−1)!.
The Gamma function extends the factorial pattern from positive integers to positive real values. The page returns both Γ(x) and ln Γ(x), using a bounded numerical approximation for stable browser results.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Input x — minimum 1.0E-6; maximum 170
Worked example
| Input | Value |
|---|---|
| Input x | 5 |
Γ(5)=24; ln Γ(5)≈3.17805.
Assumptions and limits
- x is positive and within the finite-result bound shown by the form.
- The result is an approximation in floating-point arithmetic.
- Negative non-integer continuation, complex arguments, and statistical inference are not modeled.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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