Iota!
Which of the following is equal to Γ ( i + 1 ) ?
Notations:
- i = − 1 is the imaginary unit .
- Γ ( ⋅ ) denotes the Gamma function .
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1 solution
@Md Zuhair you should mention that factorial symbol can only be used for whole numbers...
This is similar to what we discussed last night. :)
Factorials can be used for complex numbers as well. The gamma function is one such function that can give it for whatever complex number you may assume. :-) (It was a proper thing to write the non-negative factorial function but please update your solution accordingly by inserting 'non-negative factorial'.)
Remark:
i ! = Γ ( i + 1 ) = ∫ 0 1 ln i ( t 1 ) d t ≈ 0 . 4 9 8 0 1 5 6 6 8 − 0 . 1 5 4 9 4 9 8 2 8 i
If we use the Gamma function definition of the factorial then we can find a unique value for any z ! , z ∈ C . Here is a discussion specifically about i ! .
You may have to add something like "Assume that the non-negative integer definition of the factorial function applies here" to avoid any reports.
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Sir do you have Whats app? If so , then if you dont mind , can you share your number?
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are u an RMO aspirant?
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@Ayush G Rai – No. I never was... I prepared for rmo in 2 weeks... and I also dont do rmo pronlems now to keep my self upgraded. . So I dont consider myself to be a rmo aspirant.
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@Md Zuhair – same over here but i saw that u interested in it before
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@Ayush G Rai – No.. its not true that I am totally uninterested .. last year I was. Very reluctanr T to give rmo. Now if I see those types of sums I like to do them
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@Md Zuhair – Or rather try them
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@Md Zuhair – would u like to join my RMO preparation team
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@Ayush G Rai – Ya.. where is it?
@Ayush G Rai – Sorry to interrupt , but even I would like to join, if possible for you.
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@Ankit Kumar Jain – u can give ur email id if u want to join.
@Ayush G Rai – Study.. join About.. he is RMO State level topper in jharkhand.
No, I don't have WhatsApp, (I had to google what it even is :)). Sorry. :(
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@Brian Charlesworth – Okay. can we communicate over emails? for that we need emails. My email is mdzuhair66@gmail.com.. if want you can email me here to let me know your email so that we could communicate
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@Md Zuhair – I've always preferred to restrict my communication with the Brilliant community to notifications on the Brilliant site alone. It just makes my life a little simpler, haha. :)
Isn't gamma a popular function being played with complex numbers?
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Yes it is, Why?
@Md Zuhair Hey, it is no use if there's a person who doesn't know a gamma function. Like me. :)
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who said every question is made thinking of curriculum. I loved maths, i learnt gamma function thats it bro. chill
This cannot be found as the factorial symbol can only be used for Whole Numbers
Factorials can used only for Whole Number