Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.1464)

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=5/2, b₁>=-11/2

For fixed z and a₁=-11/2, a₂=5/2, b₁=-9/2

http://functions.wolfram.com/07.25.03.1464.01

Input Form

HypergeometricPFQ[{-(11/2), 5/2}, {-(9/2), 5}, z] == -((1/(1964187225 z^2)) (32 E^(z/2) (-1137161025 - 66891825 z - 11351340 z^2 - 2328480 z^3 - 604800 z^4 - 215040 z^5 - 122880 z^6 - 196608 z^7 + 262144 z^8) BesselI[0, z/2])) + (1/(1964187225 z^3)) (32 E^(z/2) (-4548644100 - 267567300 z + 57972915 z^2 + 9604980 z^3 + 1905120 z^4 + 470400 z^5 + 153600 z^6 + 73728 z^7 + 65536 z^8 + 262144 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]