Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.0792)

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=-11/2, a₂>=-11/2

For fixed z and a₁=-11/2, a₂=1/2, b₁>=-11/2

For fixed z and a₁=-11/2, a₂=1/2, b₁=-7/2

http://functions.wolfram.com/07.25.03.0792.01

Input Form

HypergeometricPFQ[{-(11/2), 1/2}, {-(7/2), 6}, z] == (1/(32081724675 z^3)) (32 E^(z/2) (3032429400 + 2697970275 z + 1480539060 z^2 + 1690185420 z^3 + 2910600 z^4 + 1174320 z^5 + 752640 z^6 + 1342464 z^7 - 2015232 z^8 + 163840 z^9) BesselI[0, z/2]) - (1/(32081724675 z^4)) (32 E^(z/2) (12129717600 + 10791881100 z + 6301209915 z^2 + 3087772380 z^3 + 1672721820 z^4 - 2205000 z^5 - 814800 z^6 - 436224 z^7 - 427008 z^8 - 1851392 z^9 + 163840 z^10) 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]