Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.1198)

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=3/2, b₁>=-11/2

For fixed z and a₁=-11/2, a₂=3/2, b₁=-1/2

http://functions.wolfram.com/07.25.03.1198.01

Input Form

HypergeometricPFQ[{-(11/2), 3/2}, {-(1/2), 5}, z] == -((1/(218243025 z^2)) (32 E^(z/2) (1964655 + 2474010 z - 5093550 z^2 - 18627840 z^3 + 54044880 z^4 - 31227168 z^5 + 6533664 z^6 - 546560 z^7 + 15360 z^8) BesselI[0, z/2])) + (1/(218243025 z^3)) (64 E^(z/2) (3929310 + 4948020 z + 3575880 z^2 + 1091475 z^3 + 2143920 z^4 + 15549744 z^5 - 12733632 z^6 + 3005072 z^7 - 265600 z^8 + 7680 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]