Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.4116)

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=2, b₁>=-11/2

For fixed z and a₁=-9/2, a₂=2, b₁=1

http://functions.wolfram.com/07.25.03.4116.01

Input Form

HypergeometricPFQ[{-(9/2), 2}, {1, 6}, z] == -((1/(43648605 z^3)) (32 E^(z/2) (90720 + 116235 z + 85995 z^2 - 1323000 z^3 + 2698920 z^4 - 1474512 z^5 + 303024 z^6 - 25152 z^7 + 704 z^8) BesselI[0, z/2])) + (1/(43648605 z^4)) (32 E^(z/2) (362880 + 464940 z + 355320 z^2 + 178605 z^3 - 105840 z^4 + 1609032 z^5 - 1207104 z^6 + 278928 z^7 - 24448 z^8 + 704 z^9) 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]