I Guidance Requested on Inductance Formula for Solenoid

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The formula for the self-inductance of a finite solenoid is presented as L = (μ(o)* N^2*A * {√(a^2+ l^2) - a} )/l^2, where 'a' is the radius of each turn and 'l' is the length of the solenoid. The user is struggling to understand the derivation of this formula and is seeking guidance on the geometric considerations involved. They also inquire about the textbook source and whether there are other references that explain the derivation. Additionally, the discussion highlights that calculating inductance for finite-length solenoids can be complex, with various empirical formulas available. Clarification on these points would greatly assist in understanding the topic.
warhammer
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In my textbook on EM, the formula for self inductance of a finite solenoid is given as:

L= (μ(o)* N^2*A * {√(a^2+ l^2) - a} )/l^2 where a=Radius of each turn, l=length of solenoid.

I am having trouble and extreme difficulty in trying to ascertain how this formula was derived in the book and what kind of geometry. They have not provided any explanations and simply stated the same.

I request guidance/hint from PF Members as to how this formula was derived.
 
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Which textbook is it? Does it point to other textbooks/papers, where the formula is derived?
 
I believe that for a finite length solenoid there is a problem with calulating inductance and so there are several emprical formulas available.
 
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