What is the proof for this?

I was learning calculus and it seemed very interesting than Olympiad topics like Algebra, NT, Geometry and Combinatorics.

But I was struck here. I used this relation many times. But I don't know the proof for this. I hovered internet for over four days continuously but can't find it anywhere? Please help me to know the proof for this relation.

Please please make me know about this proof. Atleast please send me the link where I can get the proof for this.

#Calculus #DigammaFunction

Easy Math Editor

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.
Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.

Markdown	Appears as
`italics` or `_italics_`	italics
`bold` or `__bold__`	bold
- bulleted - list	bulleted list
1. numbered 2. list	numbered list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1 paragraph 2	paragraph 1 paragraph 2
`[example link](https://brilliant.org)`	example link
`> This is a quote`	This is a quote
# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"	# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"

Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

@Kartik Sharma @Upanshu Gupta @Calvin Lin @Aditya Kumar @Tanishq Varshney @Aman Raimann Please help me.

Surya Prakash - 5 years, 8 months ago

Well, I will ask you first what have you tried. Don't forget the definition of digamma and move on with the proof and I think you'll prove it.

Kartik Sharma - 5 years, 8 months ago

Actually digamma function is defined as

But how can this help to prove digamma function.

Surya Prakash - 5 years, 8 months ago

Hey man u r really awesome at calculus. Where can I contact u? I see u r in our hangouts group but u r inactive there.

Aditya Kumar - 5 years, 8 months ago

I learnt it from here.

Aditya Kumar - 5 years, 8 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$