Mathematical constants | Integrals

Sophomore's dream

In mathematics, the sophomore's dream is the pair of identities (especially the first) discovered in 1697 by Johann Bernoulli. The numerical values of these constants are approximately 1.291285997... and 0.7834305107..., respectively. The name "sophomore's dream" is in contrast to the name "freshman's dream" which is given to the incorrect identity (x + y)n = xn + yn. The sophomore's dream has a similar too-good-to-be-true feel, but is true. (Wikipedia).

Sophomore's dream
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This Works Out?! An Unbelievably Satisfying Closed Form for the Generalized Sophomore's Dream!

Help me create more free content! =) https://www.patreon.com/mathable Merch :v - https://teespring.com/stores/papaflammy https://www.amazon.com/shop/flammablemaths https://shop.spreadshirt.de/papaflammy Become a Member of the Flammily! :0 https:

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The Integral of your Dreams (or Nightmares)

This integral is super similar to the integral of x^x (but it's x^-x). This is known as the Sophomore's Dream integral because the answer is dreamlike! Some of the links below are affiliate links. As an Amazon Associate I earn from qualifying purchases. If you purchase through these li

From playlist Integrals, Integrals, Integrals

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Integrating the boi of your Putnam dreams ( Sophomore's dream: Integral x^-x from 0 to 1 )

Help me create more free content! =) https://www.patreon.com/mathable Merch :v - https://teespring.com/de/stores/papaflammy https://shop.spreadshirt.de/papaflammy Let us integrate a pure classic! This Integral is called Sophomore's dream sometimes. Be prepared for some

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Integrating the boi of your Putnam Dreams - Sophomore's Dream Reloaded!

Help me create more free content! =) https://www.patreon.com/mathable Merch :v - https://teespring.com/de/stores/papaflammy https://www.amazon.com/shop/flammablemaths https://shop.spreadshirt.de/papaflammy Original dream: https://www.youtube.com/watch?

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You're Dreaming

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Related pages

Series (mathematics) | Johann Bernoulli | List of integrals of logarithmic functions | Gamma function | Integration by substitution | Natural logarithm | Integration by parts | Exponential function | Constant of integration | Identity (mathematics) | Power series | Freshman's dream | Uniform convergence | Mathematical induction | Euler integral