q-polygamma function

Article summary

mathematical special function in the gamma family

Key claims

1. P2534: <math class="mwe-math-element mwe-math-element-inline mathjax_ignore" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><msub><mi>γ</mi><mrow data-mjx-texclass="ORD"><mi>q</mi></mrow></msub><mo stretchy="false">(</mo><mi>z</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">−</mo><mi>ln</mi><mo>&#x2061;</mo><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">−</mo><mi>q</mi><mo stretchy="false">)</mo><mo stretchy="false">+</mo><mi>ln</mi><mo>&#x2061;</mo><mi>q</mi><munderover><mo movablelimits="false" stretchy="false">∑</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>n</mi><mo stretchy="false">=</mo><mn>0</mn></mrow></mrow><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">∞</mi></mrow></munderover><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><msup><mi>q</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>n</mi><mo stretchy="false">+</mo><mi>z</mi></mrow></mrow></msup></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>1</mn><mo stretchy="false">−</mo><msup><mi>q</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>n</mi><mo stretchy="false">+</mo><mi>z</mi></mrow></mrow></msup></mrow></mrow></mfrac></mrow></mstyle></mrow></math> — source: Wikidata · confidence 0.95
2. P2671: /g/11b6d_dyzl — source: Wikidata · confidence 0.95
3. P2812: q-PolygammaFunction — source: Wikidata · confidence 0.95
4. P31: Q867707 — source: Wikidata · confidence 0.95
5. P6104: Q8487137 — source: Wikidata · confidence 0.95

Discussion questions

1. Summarise the article in your own words. Which single claim would you verify first, and why?
2. The record states that the P2534 is "<math class="mwe-math-element mwe-math-element-inline mathjax_ignore" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><msub><mi>γ</mi><mrow data-mjx-texclass="ORD"><mi>q</mi></mrow></msub><mo stretchy="false">(</mo><mi>z</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">−</mo><mi>ln</mi><mo>&#x2061;</mo><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">−</mo><mi>q</mi><mo stretchy="false">)</mo><mo stretchy="false">+</mo><mi>ln</mi><mo>&#x2061;</mo><mi>q</mi><munderover><mo movablelimits="false" stretchy="false">∑</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>n</mi><mo stretchy="false">=</mo><mn>0</mn></mrow></mrow><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">∞</mi></mrow></munderover><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><msup><mi>q</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>n</mi><mo stretchy="false">+</mo><mi>z</mi></mrow></mrow></msup></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>1</mn><mo stretchy="false">−</mo><msup><mi>q</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>n</mi><mo stretchy="false">+</mo><mi>z</mi></mrow></mrow></msup></mrow></mrow></mfrac></mrow></mstyle></mrow></math>". What evidence would count against this claim?
3. The record states that the P2671 is "/g/11b6d_dyzl". What evidence would count against this claim?
4. The record states that the P2812 is "q-PolygammaFunction". What evidence would count against this claim?
5. The record states that the P31 is "Q867707". What evidence would count against this claim?
6. The record states that the P6104 is "Q8487137". What evidence would count against this claim?
7. Which claim in this article is most likely to be revised as the sources update? How would you check its current status?
8. If two sources disagreed about one of these facts, what would you need in order to trust one over the other?

Bibliography

No sources recorded.