Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.4849)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For integer and half-integer parameters and fixed z

For fixed z and a₁=9/2, b_1`>=-11/2

For fixed z and a₁=9/2, b₁=-11/2

http://functions.wolfram.com/07.22.03.4849.01

Input Form

HypergeometricPFQ[{9/2}, {-(11/2), -(5/2)}, -z] == (1 - (128 z)/55 + (16 z^2)/11 - (512 z^3)/693 + (512 z^4)/2475 + (4096 z^5)/22275 - (4096 z^6)/334125) Cos[2 Sqrt[z]] + (1/16372125) (2 Sqrt[z] (16372125 - 16272900 z + 7938000 z^2 - 5080320 z^3 - 1881600 z^4 - 752640 z^5 + 4096 z^6) Sin[2 Sqrt[z]])

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,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},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]