Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.amwj)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]

Specific values

For integer and half-integer parameters and fixed z

For fixed z and a₁=9/2, a₂>=9/2

For fixed z and a₁=9/2, a₂=11/2, b₁>=-11/2

For fixed z and a₁=9/2, a₂=11/2, b₁=-11/2

http://functions.wolfram.com/07.25.03.amwj.01

Input Form

HypergeometricPFQ[{9/2, 11/2}, {-(11/2), -(11/2)}, z] == (1/10721859080625) (10721859080625 E^z - 1949428923750 E^z z + 4332064275000 E^z z^2 + 5127749550000 E^z z^3 + 18778172490000 E^z z^4 + 165941048196000 E^z z^5 + 12326515806528000 E^z z^6 + 850285835118720000 E^z z^7 + 6033130095263040000 E^z z^8 + 14208488517750912000 E^z z^9 + 15660652688058470400 E^z z^10 + 9518532533675827200 E^z z^11 + 3503189220959232000 E^z z^12 + 827059117860864000 E^z z^13 + 129831438178713600 E^z z^14 + 13832157513646080 E^z z^15 + 1007749507645440 E^z z^16 + 49926271795200 E^z z^17 + 1644783206400 E^z z^18 + 34304163840 E^z z^19 + 407896064 E^z z^20 + 2097152 E^z z^21)

Standard Form

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MathML Form

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Rule Form

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Date Added to functions.wolfram.com (modification date)

2007-05-02

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]