Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.3906)

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=3/2, b₁>=-11/2

For fixed z and a₁=-9/2, a₂=3/2, b₁=-5/2

http://functions.wolfram.com/07.25.03.3906.01

Input Form

HypergeometricPFQ[{-(9/2), 3/2}, {-(5/2), 6}, z] == (1/(218243025 z^3)) (32 E^(z/2) (-145945800 - 88783695 z - 30062340 z^2 + 888300 z^3 + 385560 z^4 + 261120 z^5 + 486912 z^6 - 761856 z^7 + 81920 z^8) BesselI[0, z/2]) - (1/(218243025 z^4)) (32 E^(z/2) (-583783200 - 355134780 z - 138492585 z^2 - 34825140 z^3 - 661500 z^4 - 263400 z^5 - 148992 z^6 - 152064 z^7 - 679936 z^8 + 81920 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]