Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.aj08)

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=5/2, a₂>=5/2

For fixed z and a₁=5/2, a₂=7/2, b₁>=-11/2

For fixed z and a₁=5/2, a₂=7/2, b₁=-11/2

http://functions.wolfram.com/07.25.03.aj08.01

Input Form

HypergeometricPFQ[{5/2, 7/2}, {-(11/2), 1}, z] == (1/467775) (E^(z/2) (467775 - 978075 z + 936900 z^2 - 742500 z^3 + 637200 z^4 - 761040 z^5 + 2338560 z^6 + 5997312 z^7 + 2928384 z^8 + 533760 z^9 + 39936 z^10 + 1024 z^11) BesselI[0, z/2]) + (1/467775) (E^(z/2) (462375 z - 545400 z^2 + 445500 z^3 - 360000 z^4 + 357840 z^5 - 580608 z^6 + 3757824 z^7 + 2451456 z^8 + 495360 z^9 + 38912 z^10 + 1024 z^11) BesselI[1, z/2])

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]